THE 

NEW  BUSINESS 
ARITHMETIC 


REVISED  EDITrON 


LIBRARY 

OF  THE 

UNIVERSITY  OF  CALIFORNIA 

GIFT    OF 


Class 


THE  NEW 

Business  Arithmetic 


A  TREATISE  ON 


Commercial  Calculations 


REVISED  EDITION 


J.  A.  LYONS  &  COMPANY 

NEW  YORK  CHICAGO 


6 


APR    4   19H 
GIFT 


COPYRIGHT.  1906, 

BY 
POWERS  &  LYONS 


PREFACE 


Since  the  great  majority  of  those  who  study  Arithmetic  need 
to  use  it  in  the  transaction  of  the  practical  affairs  of  life,  a  text- 
book on  the  subject,  should  be  especially  practical.  It  has  been 
the  aim  in  the  preparation  of  this  work  to  represent  the  business 
methods  of  the  times.  While  a  few  problems  are  intended  to 
illustrate  some  principle,  by  far  the  greater  number  show  the 
application  of  Arithmetic  to  the  actual  business  transactions  of 
the  day.  In  this  practical  character  we  believe  the  book  will  be 
found  unequaled. 

The  principles  of  each  successive  topic  are  carefully  developed 
by  appropriate  exercises,  so  graded  that  the  mind  of  the  student 
must  inevitably  grasp  the  relations  of  the  whole  subject,  and 
when  the  work  is  completed,  comprehend  it,  not  as  a  mass 
of  loosely-connected  details,  but  as  a  unified  whole. 

Since  good  methods  economize  time  and  energy,  secure  rapid- 
ity and  accuracy  in  calculation,  and  strengthen  the  reasoning 
powers,  the  aim  has  been  to  present  each  subject  in  the  most 
clear  and  concise  manner,  showing  the  reason  for  every  operation 
performed,  in  order  that  the  student  may  learn  to  rely  upon  the 
principle  involved  and  not  merely  seek  for  a  result. 

The  treatment  of  the  fundamental  rules  of  Arithmetic  has 
been  made  simple,  and  is  free  from  all  effort  to  exalt  these  rules 
into  complex  and  difficult  propositions.  A  clear  explanation, 
followed  by  an  abundance  of  well  graded  problems,  will  enable 
the  pupil  to  readily  master  the  foundation  work  of  Arithmetic. 

The  work  in  Fractions  is  made  plain  by  giving  brief,  clear 
and  accurate  definitions,  and  simple,  concise  and  logical  solutions 
of  concrete  problems.  Compound  Numbers  are  explained  by 
showing  their  relation  to  simple  numbers,  while  the  exercises 
and  problems  deal  with  facts  found  in  every-day  life. 

The  subject  of  Percentage  and  its  applications  is  made  most 

3 

- .   -  -    -: 


4  PREFACE 

thorough  and  practical.  A  system  of  analysis  is  employed  which 
must  inevitably  fix  the  principles  clearly  in  the  mind  of  the 
learner. 

Equation  of  Payments,  Averaging  Accounts  and  Partnership 
have  been  emphasized  according  to  the  demand  of  business. 

That  the  reasoning  powers  of  the  pupil  may  be  strengthened 
and  his  ability  to  think  independently  of  pencil  and  tablet  may  be 
increased,  several  hundred  problems  for  oral  solution  have  been 
added.  The  work  undoubtedly  now  contains  an  abundance  of 
material,  not  only  for  giving  facility  in  computations,  but  for 
correct  training  in  arithmetical  thought. 

We  have  made  an  earnest  effort  to  present  such  a  work  to 
teachers  and  students  as  will  meet  with  their  approval  and  suit 
their  wants.  We  believe  by  a  thorough  study  of  the  work  young 
men  and  women  will  go  out  into  the  business  world  intelligent 
persons  with  ability  to  apply  their  knowledge. 

THE  AUTHOR. 


CONTENTS 


PAGE: 

DEFINITIONS  7 

NOTATION  AND  NUMERATION 8 

ADDITION 13 

SUBTRACTION 18 

MULTIPLICATION 22 

DIVISION    30 

FACTORING  37 

CANCELLATION   ' 38 

GREATEST  COMMON  DIVISOR 40 

LEAST  COMMON  MULTIPLE 41 

FRACTIONS • 44 

Reduction   46 

Addition    : 52. 

Subtraction     55 

Multiplication 58 

Division    64 

DECIMAL    FRACTIONS 74 

Reduction   77 

Addition    79 

Subtraction  81 

Multiplication    82 

Division    83 

COMPOUND    NUMBERS 85 

UNITED  STATES  MONEY 86 

Addition 87 

Subtraction 89 

Multiplication    90 

Division    91 

SHORT  METHODS 92. 

BILLS    • 97 

REDUCTION  OF  DENOMINATE  NUMBERS 105 

United  States  Money 105 

Canada   Money 105 

English  Money 106 

Avoirdupois  Weight 108 

Trov  Weight \ 110 

Apothecaries'  Weight Ill 

Comparison  of  Weights 112 

Long  Measure 113 

Surveyors'  Long  Measure 115 

Square  Measure 115 

Board    Measure 118 

Surveyors'  Square  Measure 119 

Cubic   Measure 123 

Liquid  Measure 125 

Apothecaries'  Fluid  Measure 126 

Dry    Measure 126 

Comparison  of  Dry  and  Liquid  Measures 127 

Time    128 

Circular  Measure 130' 

REDUCTION  OF  DENOMINATE  FRACTIONS 134- 

6 


6  CONTENTS 

DENOMINATE  NUMBERS — Addition 139 

Subtraction     141 

Multiplication    143 

Division     144 

LONGITUDE  AND  TIME 146 

RATIO 154 

Proportion    155 

Compound    Proportion 158 

MEASUREMENTS  USED  IN   BUSINESS 161 

PERCENTAGE    167 

PROFIT    AND    Loss 183 

MARKING   GOODS 190 

TRADE  DISCOUNT 193 

BILLS 197 

COMMISSION   205 

INSURANCE    • 213 

Fire    Insurance 214 

Marine  Insurance 217 

Life  Insurance 219 

INTEREST 225 

Sixty  Days  Method 232 

Six  Per  Cent  Method 233 

Cancellation    Method 235 

Common  Bankers'  and  Exact  Interest  Compared 236 

Annual    Interest 243 

Compound   Interest 245 

COMMERCIAL  PAPER 250 

Partial  Payments 255 

Annual  Interest,  with  Partial  Payments 260 

TRUE    DISCOUNT % 261 

BANK  DISCOUNT 264 

STOCKS  AND  BONDS 268 

EXCHANGE    277 

Domestic    Exchange 278 

Foreign  Exchange 281 

BANKS  AND  BANKING 284 

National    Banks 284 

Savings    Banks 287 

TAXES    292 

CUSTOMS  OR  DUTIES • 295 

EQUATION  OF  ACCOUNTS 299 

CASH  BALANCE 311 

PARTNERSHIP 313 

INVOLUTION    328 

EVOLUTION. 329 

Square    Root 330 

Applications  of  Square  Root 332 

Cube   Root 334 

Applications  of  Cube   Root 

MENSURATION    338 

Plane    Figures 339 

Solids     341 

Metric    System 345 

Value  of  Moneys 350 

STATUTORY    WEIGHTS!  .  ...  352 


ARITHMETIC 


DEFINITIONS 

1.  Arithmetic  is  the  science  of  numbers  and  their  use. 

2.  A  Unit  is  a  single  thing ;  as,  one,  one  man,  one  horse. 

3.  A  Number  is  one  or  more  units ;  as  1,  3,  9,  6  boys. 

4.  The  Unit  of  a  Number  is  one  of  the  kind  expressed  by 
the  number.     The  unit  of  9  is  1,  the  unit  of  20  feet  is  1  foot. 

5.  An  Integer  is  a  whole  number. 

6.  Like    Numbers   are    those    which    are    composed    of    the 
same  kinds  of  units.     Thus  25  and,  34 ;  3  yards  and  10  yards. 

7.  An  Abstract  Number  is  one  used  without  reference  to  any 
particular  thing  or  quantity.     Thus  15;  64;  280. 

8.  A  Concrete  Number  is  one  used  with  reference  to  some 
particular  thing  or  quantity.     Thus  25  dollars ;  14  days ;  100  men. 

Concrete   numbers   are   called   denominate   numbers   because   the   de- 
nomination or  kind  is  named. 

9.  A  Sign  is  a  character  used  to  indicate  an  operation,  or  ex- 
press the  qualities  or  relations  of  numbers. 

A  Solution  is  a  process  of  computation  used  to  obtain  a  re- 
quired result. 

10.  A  Problem  is  a  question  for  solution. 

llT  An  Example  is  a  problem  solved,  illustrating  a  principle 
or  rule. 

12.  A  Principle  is  a  truth  upon  which  the  solution  is  founded. 

13.  An  Analysis  is  a  statement  of  the  successive  steps  in  a 
solution. 

14.  An  Explanation  is  a  statement  of  the  reasons  for  the 
manner  of  solving  a  problem. 

15.  A  Rule  is  a  direction  for  solving  problems. 

7 


NOTATION  AND  NUMERATION 

16.  Notation  is  the  art  of  writing  numbers  by  means  of 
characters. 

17.  Numeration  is  the  art  of  reading  numbers  written  by 
characters. 

Two  systems  of  Notation  are  in  general  use:  the  Roman  and 
the  Arabic.  The  Roman  is  supposed  to  have  been  invented  by 
the  Romans  and  employs  seven  capital  letters  to  express  num- 
bers. The  Arabic  is  said  to  be  derived  from  the  Arabs  and  em- 
ploys ten  characters  called  figures. 

ARABIC  NOTATION 

18.  Figures  are  characters  used  to  represent  numbers. 
There  are  ten  figures : 

0,       1,       2,       3,       4,       5,       6,       7,       8,       9. 

Zero,      One,      Two,     Three,    Four,      Five,      Six,     Seven,     Eight,    Nine. 

The  Figure  0,  Zero  or  Cipher,  expresses  no  units,  or  nothing, 
when  standing  alon,e.  The  other  nine  figures  express  the  num- 
ber of  units  shown  by.  their  names.  These  figures  are  called 
digits. 

19.  To  express  numbers  greater  than  nine  and  less  than  one 
hundred,  two  figures  are  written  side  by  side ;  as,  thirty-six,  36 ; 
seventy-two,  72. 

20.  To  express  numbers  greater  than  ninety-nine,  three  or 
more  figures  are  written  side  by  side ;  as,  one  hundred  eighty-five, 
185 ;  two  thousand  six  hundred  twenty-four,  2624. 

21.  When  figures  are  written  side  by  side,  the  one  at  the  right 
expresses  units  or  ones,  the  next  tens,  the  next  hundreds,  the 
next  thousands,  etc. 

22.  The  Simple  Value  of  a  figure  is  the  value  it  expresses 
when  standing  alone,  or  in  unit's  place ;  as  3,  7,  9. 

23.  The  Local  Value  of  a  figure  is  the  value  it  expresses 
when  used  with  other  figures  to  represent  a  number, 

8 


NOTATION  AND   NUMERATION  9 

In  the  number  345,  the  figure  5  expresses  a  simple  value,  and 
the  figures  3  and  4  express  local  values. 

24.  The  Order  of  a  Unit  takes  its  name  from  the  place  it 
occupies.  A  figure  in  the  first  place  expresses  units  of  the  first 
order ;  in  the  second  place,  units  of  the  second 'order,  etc. 

When  a  figure  stands  in  the  second  place  it  represents  tens; 
in  the  third  place  hundreds ;  in  the  fourth  place  thousands,  etc. 

One  ten  is  written 10 

One  ten  and  four,  fourteen 14 

Two  tens,   twenty 20 

Two  tens  and  seven,  twenty-seven 27 

Three  tens,   thirty . ; 30 

One  hundred,  one  ten  and  seven,  one  hundred  seventeen.  . .  .  117 
Three  hundred,  five  tens  and  nine,  three  hundred  fifty-nine.  .  359 
Six  thousand,  five  hundreds,  nine  tens  and  two,  is  read,  six 

thousand  five  hundred  ninety-two 6592 

NOTE. — In  reading  whole  numbers  the  word  AND  should  not  be  used. 
Thus,  seven  hundred  fifty-four,  not  seven  hundred  and  fifty-four. 

Copy  and  read  the  following  numbers : 

'  1.  297        5.  1790  9.  3096 

2.  472        6.  4607  10.  7006 

3.  685        7.  9218  11.  8200 

4.  920        8.  2030  12.  6303 

Write  the  following  in  figures : 
13.     One  hundred  forty-six. 
14-     Seven  hundred  ten. 

15.  Six  hundred  three. 

16.  Two  hundred  ninety. 

77.  Five  hundred  thirty-eight. 

18  Three  thousand  seven  hundred  nineteen. 

19.  Six  thousand  nine  hundred  twenty-seven. 

20.  Four  thousand  sixty-four. 

21.  Seven  thousand  four  hundred  one. 

22.  Five  thousand  forty. 

23.  Nine  thousand  six  hundred  ninety-six. 
24>  Eight  thousand  eight  hundred. 


10 


NEW   BUSINESS   ARITHMETIC 


25.  Seven  units  of  the  first  order  and  two  of  the  second. 

26.  Nine  units  of  the  fourth  order,  three  of  the  third, 

two  of  the  second  and  one  of  the  first. 

27.  Five  units  of  the  third  order,  one  of  the  first. 

28.  Six  units  of  the  fourth  order,  seven  of  the  second, 

two  of  the  first. 

25.  For  convenience,  figures  are  arranged  in  periods  of  three 
places  each ;  the  first  three  at  the  right  being  called  units  or  one's 
period;  the  next  three  the  thousand's  period;  the  next  three  the 
million's  period,  etc. 


Quadrillions.    Trillions,        Billions, 
6th  period.    5th  period,    4th  period, 


TABLE 

Millions, 
3d  period, 


Thousands. 
2d  period, 


546, 


897, 

to  t-i  o 


534, 

,000  -a 


ffi  HO 
e    rt    c 


3^3: 

o-  p   ct 

a-  o 

•2   2.  3 


§  s  a 


i§ 


H  W 

3  g 


-- 


3  § 


2   6 

05   Or 
3*   3* 


i!l 


Units, 
1st  period,     Periods. 

9  8  ~~T?  Figures. 
•  %  %  £     Places. 

*Z$ 


General  Principles 

1.  Ten  units  of  any  order  equal  one  unit  of  the  next  higher 
order..  .Ten  units  equal  one  ten;  ten  tens  equal  one  hundred;  ten 
hundreds  equal  one  thousand,  etc. 

2.  Removing  a  figure  one  place  to  the  left  increases  its  value 
ten  times.     Removing  a  figure  one  place  to  the  right  decreases  its 
-value  ten  times. 

To  Write  Numbers 


a.  Begin  at  the  left  and  write  the  figures  belonging  to  the 
highest  period. 

b.  Write  the  hundreds,  tens  and  units  of  each  period  in  their 
order,  putting  a  cipher  in  the  place  of  any  order  that  is  omitted. 


NOTATION   AND   NUMERATION  11 

To  Read  Numbers 

a.  Begin  at -the  right  and  point  off  the  numbers  into  periods 
of  three  figures  each. 

b.  Begin  at  the  left  and  read  each  period  separately,  giving 
the  name  to  each  period  except  the  last. 

Read  the  following: 

1.  384  5.       136042  9.         147002001 

2.  9328  6.       100420  10.       3073640240 

3.  11765  7.     9793642  11      73260479142 

4.  29470  8.     3106053  12.     48600752052 

Write  the  following  numbers : 

13.  Ninety-seven. 

14.  Three  hundred  sixty-eight. 

15.  Two  thousand  four  hundred  seventy-five. 

16.  Thirty-seven  thousand  one  hundred  ninety-six. 

17.  One     hundred     thirty-six     thousand     three     hundred 

twenty-seven. 

18.  Five   million   three   hundred   six   thousand   five   hun- 

dred three. 

ROMAN  NOTATION 

26.  Roman   Notation   employs   seven   capital   letters   to   ex- 
press numbers,  as  follows : 

Letters  I,  V,   X,  L,     C,      D,       M.  ' 
Values  1,    5,  10,  50,  100,  500,  1000. 

These  letters  may  be  combined  to  express  numbers  according 
to  the  following  principles : 

1.  Repeating  a  letter  repeats  its  value. 

Thus,  II  represents  2 ;  XX,  20 ;  CCCC,  400 ;  DD,  1000. 

2.  When  a  letter  is  placed  after  one  of  greater  value,  its  value 
is  to  be  added  to  that  of  the  greater. 

Thus,  VI  represents  6 ;  XV,  15 ;  XXI,  21 ;  DC,  600 ;  DCX, 
610. 

3.  When  a  letter  is  placed  before  one  of  greater  value,  its 
value  is  to  be  taken  from  the  greater. 

Thus,  IX  represents  9 ;  XL,  40 ;  XC,  90 ;  CD,  400. 


12 


NEW   BUSINESS   ARITHMETIC 


4-  When  a  letter  of  any  value  is  placed  between  two  letters, 
each  of  greater  value,  its  value  is  taken  from  the  sum  of  the  other 
two. 

Thus,  XIV  represents  14 ;  XIX,  19 ;  LIX,  59 ;  CXL,  140. 
5.     A  bar  placed  over  a  letter  increases  its  value  one  thousand 
times. 

Thus,  X~ represents  10000  ;lCL,  40000;  CD",  400000. 

27.  TABLE   OF    ROMAN    NOTATION 


Roman 

Arabic. 

Roman. 

Arabic. 

Roman. 

Arabic. 

Roman. 

Arabic. 

I, 

1. 

IX, 

9. 

XX, 

20. 

xc, 

90. 

II, 

2. 

x, 

10. 

XXI, 

21. 

c, 

100. 

III, 

3. 

XIII, 

13. 

XXX, 

30. 

ccc, 

300. 

IV, 

4. 

XIV, 

14. 

XL, 

40. 

D, 

500. 

V, 

5. 

XV, 

15. 

L, 

50. 

DCC, 

TOO. 

VI, 

6. 

XVIII, 

18. 

LX, 

60. 

M, 

1000. 

VIII, 

8. 

XIX, 

19. 

LXXX, 

80. 

MD, 

1500. 

28.  Express  by  Roman  notation : 


1.  Eighteen. 

2.  Twenty-three. 
8.  Fifty-eight. 

4.  Ninety-nine. 

5.  Eighty-four. 


6.  One  hundred  eighty-eight. 

7.  One  hundred  ninety-nine. 

8.  Five  hundred  seventeen. 

9.  Six  hundred  forty-five. 
10.  Seven  hundred  sixty-one. 


11. 
12. 
13. 
14- 
15. 


428. 

975. 

1116. 

23480. 

76103. 


29.  Express  by  Arabic  notation : 


1.  XXIX. 

2.  LXVIII. 
8.  CLXIV. 
4.  CXXIV. 

5.  cccxxxm. 


6.  DCLVI. 

7.  MDLVIII. 

8.  CLIL 

9.  VDXXII. 
10.  DX. 


11.  CXIX. 

12.  XICCIV. 

13.  MMDCXVIIL 

14.  VDXLIV. 

15.  MDLXXII. 


ADDITION 

30.  Addition  is  uniting  two  or  more  numbers  into  one  num- 
ber. 

31.  The  Sum  or  Amount  is  the  number  obtained  by  adding. 

32.  The  Sign  of  addition  is  an  upright  cross  +,  and  is  read 
plus.     When  it  is  placed  between  two  numbers,  it  shows  that 
they  are  to  be  added.     $3  +  $2  is  read  3  dollars  plus  2  dollars, 
and  means  that  2  dollars  are  to  be  added  to  3  dollars. 

The  sign  $  is  used  for  dollars,  c.  or  cts.  for  cents. 

33.  The  Sign  of  equality  is  two  horizontal  lines  =,  and  is 
read  equal  or  arc  equal  to.     2  -\-  5  =  7 is  read  2  plus  5  equal  7. 

34.  When  the  amount  of  each  column  is  less  than  ten. 

1.  A  farmer  raised  232  bushels  of  corn,  142  bushels  of  wheat 
and  223  bushels  of  oats;  how  many  bushels  did  he  raise  in  all? 

Find  the  sum  of  each  of  the  following : 


1 

2 

3 

4 

5 

6 

232 

323 

245 

312 

437 

1102 

142 

242 

321 

243 

140 

1312 

223 

324 

132 

412 

321 

4132 

597 

7.  What  is  the  sum  of  321,  142  and  323? 

8.  What  is  the  amount  of  213,  152  and  401  ? 

9.  What  is  the  sum  of  3232,  2323  and  4102  ? 

10.  I  paid  $212  for  a  wagon,  $150  for  one  horse,  $210  for 
another  horse,  and  $11  for  a  set  of  harness.  What  did  I  pay 
for  all? 

13 


14  NEW   BUSINESS    ARITHMETIC 

35.   When  the  sum  of  any  column  is  greater  than  9. 
1.  Find  the  sum  of  3164,  2247,  4234  and  3232. 

EXPLANATION.— The  sum  of  the  units  2,  4,  7  and  4  is  17 
units  or  1  ten  and  7  units ;  write  the  7  units  under  the  col- 
umn of  units  and  add  1  ten  to  the  column  of  tens.     The 
sum  of  the  tens  1,  3,  3,  4  and  6  is  17  tens  or  1  hundred  and 
2247  ^  tens;  write  the  tens  under  the  column  of  tens  and  add 

4234  the  *  hundred  to  tne  column  of  hundreds.     The  sum  of 

the  huncireds  !»  2,  2,  2  and  1  is  8  hundreds;  write  under  the 
column  of  hundreds.     The  sum  of  the  thousands  3,  4,  2  and 
19877  ^  *S  ^  thousands  or  1  ten-thousand  and  2  thousands;  write 

the  2  thousands  under  the  column  of  thousands  and  the  1 
ten-thousand  in  the  place  of  ten-thousands.  The  result 
12877  is  the  sum  required. 

1.  Units  of  the  same  order  are  written  in  the  same  column ;  and  when 
the  sum  in  any  column  is  10  or  more  than  10,  it  produces  one  or  more 
units  of  a  higher  order,  which  must  be  added  to  the  next  column.     This 
process  is  sometimes  called  "carrying  the  tens." 

2.  In  adding,  learn  to  pronounce  the  partial  results  without  naming 
the  numbers  separately;  thus  instead  of  saying  2  and  4  are  6  and  7  are  13, 
simply  pronounce  the  results  6,  13,  17,  etc. 

From  the  foregoing  examples  and  illustrations  we  deduce  the 
following : 

To  Add  Whole  Numbers 

a.  Write  the  numbers  so  that  figures  of  the  same  order  are  in 
the  same  column. 

b.  Begin  at  the  right  and  add  each  column  separately. 

c.  When  the  sum  of  any  column  is  greater  than  9,  place  the 
right-hand  figure  of  the  result  under  the  column  added  and  add 
the  remaining  figure  or  figures  to  the  next  column. 

d.  Write  at  the  left  the  sum  of  the  last  column. 

PROBLEMS 


m 

24 

(8) 
265 

432 

(5) 
1362 

to 

3420 

(V 
9416 

32 

314 

864 

1487 

1862 

3624 

46 

286 

526 

4532 

1425 

1583 

84 

627 

893 

2386 

6347 

2436 

ADDITION 


15 


,8) 

(9) 

(10) 

(11) 

(12) 

(IS) 

234 

979 

9140 

94187 

-71758 

986756 

562 

2864 

6968 

71849 

3680 

863694 

846 

52 

8947 

48197 

797 

387623 

324 

715 

7968 

89471 

36425 

890124 

118 

3680 

5392 

19478 

943628 

1369479 

462 

9289 

18364 

26480 

102154 

279562 

367 

360 

27147 

62849 

864209 

8325791 

214 

14006 

38297 

56783 

579135 

2345678 

14.  128  +  324  +  116  +  893  +  246  +  427  =  how  many? 

15.  1265  +  3482  +  2149  +  3625  +  1304  +  107  =  how 
many? 

16.  28603  +  24567  +  39042  +  16841  +  40218  =  how  many  ? 

17.  Find  the  sum  of  $347,  $962,  $375,  $842  and  $636. 

18.  What  will  be  the  amount  of  $3476,  $1924,  $4822,  $3965 
and  $7180? 

19.  Add  8765  feet,  5678  feet,  6758  feet,  7685  feet  and  3629 
feet. 

20.  Add   forty-nine,   seventy-six,   three   hundred  twenty-five, 
nine  thousand  six  hundred  thirty-three,  five  thousand  one  hun- 
dred ten  and  sixty-two  thousand  four  hundred  eleven. 

21.  Find  the  sum  of  three  hundred  seventy,  two  thousand 
eighty-one,  seven  thousand  four  hundred  sixteen,  fifty  thousand 
one  hundred  twenty-nine  and  four  hundred  forty-four  thousand 
six  hundred  ninety-three. 

22.  A  paid  $762  for  hogs,  $1869  for  cattle,  $3796  for  horses 
and  then  had  $9240  remaining.     How  much  had  he  at  first? 

28.  I  sold  six  cows  that  weighed  as  follows:  1824  pounds, 
1369  pounds,  964  pounds,  2217  pounds,  1746  pounds,  1940  pounds. 
How  many  pounds  did  they  all  weigh  ? 

24.  A  farmer  bought  four  farms.     He  paid  $3221  for  the  first, 
$5680  for  the  second,  $4216  for  the  third  and  $2645  for  the  fourth. 
How  much  did  he  pay  for  all  ? 

25.  I  paid  $212  for  a  wagon,  $154  for  one  horse,  $210  for  an- 
other horse  and  $65  for  a  set  of  harness.     What  did  I  pay  for  all  ? 


16  NEW  BUSINESS  ARITHMETIC 

26.  R.  D.  Lyman  bought  four  lots.     He  paid  $2232  for  the 
first,  $3124  for  the  second,  $1485  for  the  third  and  $2238  for  the 
fourth.     Find  the  cost  of  the  four  lots. 

27.  A  merchant  paid  $746  for  calico,  $294  for  linen,  $2864 
for  shoes,  $212  for  toys  and  $1169  for  carpets.     How  much  did 
he  pay  for  all  ? 

28.  A  farmer  raised  1278  bushels  of  corn,  1642  bushels  of 
wheat,  765  bushels  of  oats,  367  bushels  of  rye,  93  bushels  of  bar- 
ley and  160  bushels  of  buckwheat.     Find  the  number  of  bushels 
of  grain  he  raised. 

(29)       (SO)       (31)       (32)       (33)  (34) 

476  +  908  +  126  +  443  +  180  +  1265  =  x 

390  +  371  +  324  +  298  +  976  +  3428  =  x 

915  +  569  +  503  +  876  +  209  +  1456  =  x 

207  +  245  +  891  +  569  +  314  +  9234  =  x 

841  +  703  +  736  +  137  +  563  +  1867  =  x 

632  +  421  +  5.17  +  910  +  842  +  2854  =  x 

234  +  127  +  143  +  347  +  175  +  3629  =  x 

143  +  354  +  274  +  256  +  224  +  2872  =  x 

536  +  781  +  531  +  324  +  135  +  3428  =  x 

245  +  436  +  275  +  463  +  253  +  9234  =  x 


x    +    •*"    +    x     +    x     +    x    +     x     =  x 

35.  The  proprietors  of  a  college  paid  $2675  for  rent,  $6286 
for  teachers,  $824  for  school  furniture,  $269  for  lights  and  $970 
for  fuel.     Find  the  total  expense. 

36.  A   bankrupt  firm's   resources   are   cash   $740,   dry-goods 
$1965,  boots  and  shoes  $1647,  Brown's  note  $1278,  office  furniture 
$280  and  real  estate  $2394.     Find  the  total  resources  of  the  firm. 

37.  I  bought  four  horses  for  $85  each.     I  sold  the  first  for  $12 
more  than  cost,  the  second  for  $16  more  than  cost,  the  third  for 
$26  more  than  cost  and  the  fourth  for  $41  more  than  cost.     How 
much  money  did  I  receive  for  all? 

38.  A,  B,  C  and  D  form  a  partnership.     A  invests  $2640,  B 
invests  $3160,  C  invests  $1125  more  than  A  and  B  together,  and 
D  invests  as  much  as  A.  and  C  together.     How  much  4id  they  all 
invest  in  the  business  ? 


ADDITION 


17 


39.  A  stock  dealer  bought  218  sheep  for  $568,  319  hogs  for 
$1162,  123  calves  for  $2316,  24  oxen  for  $695  and  11  horses  for 
$957.     How  many  head  of  stock  did  he  buy  and  how  much  did 
they  cost? 

40.  I  sold  a  house  for  $3278  and  a  lot  for  $1360.     I  lost  $392 
on  the  house  and  $125  on  the  lot.     What  did  both  cost  me? 

41.  Find   the    sum    of    $618,    $974,    $1243,    $7896,    $20374, 
$36345,  $9289,  $33696,  $180,  $49270  and  $37025. 


(42) 

(4?) 

(44)    (45) 

(46) 

852  - 

f  895  + 

967  +  58378 

+  47114 

=  x 

734  - 

-f  766  + 

3833  +  64956 

4-  89725 

=  X 

3383  - 

f  677  + 

592  +  7895 

+  65836 

=  X 

7930  - 

-f  2814  + 

5745  +  6384 

+  85684 

=  X 

496  - 

f  5920  + 

824  +  5463 

+  78912 

'===-  X 

757  - 

•f  6782  + 

978  +   981 

+  97865 

=  X 

2183  - 

f  588  + 

684  +  4752 

+  65438 

=  X 

3652  - 

-f  676  + 

756  +  3946 

+  99914 

=  X 

1138  - 

f  983  + 

1492  +   895 

+  88827 

=  X 

2795  - 

f  1495  + 

767  +  1574 

+  77715 

==  X 

676  - 

•f  6?4  + 

4543  +  6388 

+  66624 

=  X 

764  - 

-f-  542  + 

786  +  5946 

-f  55568 

=  X 

.  842  - 

f  721  + 

692  +  7892 

+  89735 

=  X 

13798  - 

f  2987  + 

370  +  1147 

+  97814 

=  X 

X 

+   x   4- 

x  -f-  x 

i    ., 

=  X 

(47) 

(48) 

(49) 

(50) 

(5*1) 

790 

9999 

49 

123456 

213579 

965 

8989 

428 

789012 

486420 

1208 

7897 

3695 

654321 

397531 

9669 

36925 

16378 

210987 

124683 

375 

52963 

875692 

913579 

610793 

92648 

13579 

3346279 

806421 

239701 

30245 

97531 

963015 

793519 

896543 

89762 

496894 

97892 

421608 

528647 

24689 

345678 

496835 

988997 

134569 

765432 

876543 

9469358 

657893 

174682 

234567 

6543210 

642086 

798979 

212345 

98898 

9876543 

59371 

397856 

167890 

SUBTRACTION 

36.  Subtraction  is  taking  one  number  from  another. 

37.  The  Minuend  is  the  number  from  which  we  subtract. 

38.  The   Subtrahend  is  the  number  to  be  taken   from   the 
minuend. 

39.  The   Remainder   or    Difference   is   the   number   left   or 
remaining  after  subtracting. 

40.  The  Sign  of  subtraction  is  a  short  horizontal  line  — ,  and 
is  called  minus;  when  placed  between  two  numbers  it  shows  that 
the  second  is  to  be  subtracted  from  the  first.     G  --  2  is  read  6 
minus  2,  and  means  that  2  is  to  be  subtracted  from  6. 

The  minuend  and  subtrahend  must  be  like  numbers;  thus,  5  dollars 
from  9  dollars  leave  4  dollars ;  5  apples  from  9  apples  leave  4  apples ;  but 
it  would  be  absurd  to  say  5  apples  from  9  dollars,  or  5  dollars  from  9 
apples. 

41.  When  each  -figure  in  the  minuend  is  greater  than  its  cor- 
responding figure  in  the  subtrahend. 

1.  From  958  subtract  324. 

SOLUTION 

MINUEND  958 

SUBTRAHEND  324 

DIFFERENCE  OR 
REMAINDER  634 

Find  the  difference  or  remainder  in  each  of  the  following : 

(2)  (3)  (4)  (5)  (6)  (7) 

67  98  86  876  676  925 

35  26  31  334  415  213 

8.  Bought  a  house  for  $547  and  sold  it  for  $315.     What  was 
my  loss? 

9.  Bought  a  farm  for  $620  and  sold  it  for  $855.     What  was 
my  gain? 

10.  A  and  B  together  bought  real  estate  for  $6985.     A  paid 
$4130.     How  much  did  B  pay? 

18 


SUBTRACTION  19 

11.  A  farmer  had  4687  bushels  of  wheat  and  sold  2380  bush- 
els.    How  many  bushels  remained? 

12.  A  man  having  96489  bricks,  sold  34375  of  them.     How 
many  had  he  left  ? 

13.  In  a  factory  86955  yards  of  cloth  were  made  in  one  week, 
of  which  36520  yards  were  sold.     How  many  yards  remained? 

4:2.  When  the  figures  in  the  minuend  are  not  all  greater  than 
the  corresponding  figures  in  the  subtrahend. 

1.  From  834  lake  378. 

SOLUTION  EXPLANATION. — Since  8  units  cannot  be  subtracted  from 

834  4  units,  add  1  ten  of  3  tens  to  units,  thus  leaving  2  tens 

378  and  giving  14  units;  8  units  from  14  units  leaves  6  units. 

Since  7  tens  cannot  be  subtracted  from  2  tens,  add  1  hun- 

456  dred  of  the  8  hundreds,  thus  leaving  7  hundreds  and  giving 

12  tens ;  7  tens  from  12  tens  leave  5  tens,  3  hundreds  from 

7  hundreds  leaves  4  hundreds.     The  result,  456,  is  the  difference  required. 

From  the  preceding  illustrations  we  have  the  following: 
To  Subtract  Whole  Numbers 

a.  Write  the  subtrahend  under  the  minuend  so  that  figures  of 
like  order  are  in  the  same  column. 

b.  Begin  at  the  right  and  subtract  each  column  separately. 

c.  If  the  lower  figure  is  greater  than  the  upper,  add  ten  to  the 
upper  figure  and  subtract  the  lower  from  it.     Take  one  from  next 
upper  figure  and  proceed  as  before. 

NOTES. — 1.  The    sum    of   the    remainder    and    subtrahend    equals    the 

minuend. 

2.  The  difference  between  the  minuend  and  remainder  equals 
the  subtrahend. 

PROBLEMS 


ft) 

873 
538 

(S)     (4)     (5)     (6)     (7) 
6423    1969    8146    3176    9076 
3862    1408    4377    2907    4567 

ft) 

5097 
3809 

ft) 

76377 

45761 

*  (10) 

67777 
46699 

(11) 
900076 
899934 

(12) 
767340 
5039 

20  NEW   BUSINESS   ARITHMETIC 

IS.  From  962  take  824. 

14.  6593  —  1807  =  how  many? 

15.  80014  — 43190  =  how  many? 

16.  From  35467  take  12479. 

17.  From  94100  take  5007. 

18.  Take  307709  from  604562. 

19.  Take  42620  from  58364. 

20.  Subtract  ten  thousand  six  hundred  forty-two  from  fifteen 
thousand  fifteen. 

21.  From  one  million  nine  thousand  six  take  twenty  thou- 
sand four  hundred. 

22.  What  is  the  difference  between  two  million  seven  thou- 
sand eighteen,  and  one  hundred  five  thousand  seventeen? 

28.  A  man  receiving  a  salary  of  $2450,  spent  for  family  ex- 
penses $968.  How  much  had  he  left? 

24.  A  farm  that  cost  $6200  was  sold  at  a  loss  of  $743.     For 
how  much  was  it  sold? 

25.  B  has  $8000  and  owes  $3749.     How  much  will  he  have 
after  paying  what  he  owes? 

26.  Bought  land  for  $9000,  sold  half  for  $6175  and  the  re- 
mainder for  $7140.     What  did  I  gain  on  the  land? 

27.  A  man  having  $10000  lost  $140.     How  much  had  he  left? 

28.  A  builder  agreed  to  build  a  church  for  $31840;  it  cost 
him  $27196.     What  was  his  gain? 

29.  A  man m  commenced  business  with  $3760,  and  at  the  end 
of  two  years  had  $6708.     How  much  did  he  gain? 

SO.  A  merchant  bought  goods  of  a  manufacturer  amounting 
to  $3180  and  paid  him  cash  amounting  to  $1892.  How  much 
does  he  still  owe  the  manufacturer? 

31.  The  distance  from  New  York  to  Queenstown  is  2890 
miles.  After  having  sailed  1640  from  New  York,  how  far  is  a 
vessel  from  Queenstown  ? 

82.  A  bought  a  lot  and  built  a  house  upon  it.  The  lot  cost 
him  $1625.  He  paid  for  carpenter  work  on  the  house  $2340 ;  for 
mason  work  $428;  for  plastering  $534;  for  plumbing  $246;  for 
painting  $186,  and  for  fencing,  grading,  etc.,  $125.  He  then 
sold  both  house  and  lot  for  $6800.  What  was  his  gain  ? 


SUBTRACTION 


21 


S3.  Find  the  balance  of  the  following  accounts:. 
DR.  MILLER  &  MILLER 


CR. 


1905 

1905 

an. 

1 

Balance, 

$125.60 

an. 

5 

Cash, 

$125.60 

an. 

4 

Mdse.,30da., 

246.24 

an. 

9 

Sight  Draft, 

325.00 

fan. 

6 

Mdse.,  2/10, 

563.42 

an. 

12 

Ret'd  Goods, 

25.94 

[an. 

9 

Mdse.,  10  da., 

327.64 

an. 

26 

Note,  30  da. 

400.00 

an. 

24 

Mdse.,  30  da., 

297.29 

34. 
DR.                             BROWNING,  KING  &  CO.                             CR. 

1905 

Feb. 
Feb. 
Feb. 
Feb. 

10 
15 

18 
26 

$300.00 
100.00 
31.65 
126.34 

1905 

Feb. 
Feb. 
Feb. 
Feb. 
Feb. 
Feb. 
Feb. 

1 
4 
6 
12 
20 
22 
24 

Balance 

$327.65 
124.00 
75.26 
24.37 
62.43 
126.34 
316.24 

35. 
DEPOSITORS'  LEDGER,  BANKERS'  NATIONAL  BANK 


Accounts 

Balance 

Deposit 

Checks  in 
Detail 

Total 
Checks 

Balance 

$     25.00 

136.00 

1.     Adams,  Wm. 

$  324.36 

$1000.00 

624.37 

$785.37 

$538.99 

324.00 

2.    Allison,  W.  K. 

462.85 

1114.60 

476.21 

***** 

***  ** 

1000.00 

3.     Brown,  F.  C. 

1142.61 

3125.00 

724.36 

? 

? 

41.25 

4.     Dennis  &  Co.  ,  W.  E. 

25.60 

784.00 

63.00 

? 

? 

216.40 

5.     Fern  Bros.  &  Co. 

284.36 

936.24 

317.42 

? 

? 

400.00 

6.     Henry  &  Henry 

924.65 

824.35 

75.63 

? 

.     ? 

369.80 

7.     Lamson  &  Bro. 

2346.80 

2143.84 

421.00 

? 

? 

8.     Mann  &  Smith 

9175.20 

924.81 

725.14 

725.14 

? 

362.24 

9.     Nero  Mfg.  Co. 

1146.24 

475.60 

436.43 

? 

? 

824.36 

10.     Mano  Eng.  Co. 

3174.38 

976.97 

642.63 

? 

? 

*****f** 

*****  ** 

•) 

? 

? 

Proof 

Bal. 

+  Dep. 

- 

Total 
Checks 

=  Bal. 

MULTIPLICATION 

43.  Multiplication  is  taking  one  number  as  many  times  as 
there  are  units  in  another.     It  is  a  short  method  of  adding  equal 
numbers ;  thus,  2  cents  +  2  cents  +  2  cents  +  2  cents  =  4X2 
cents  =  8  cents. 

44.  The  Multiplicand  is  the  number  to  be  taken ;  as,  2  cents 
in  the  above. 

45.  The  Multiplier  is  the  number  which  shows  how  many 
times  the  multiplicand  is  taken;  as,  4  in  the  above. 

46.  The  Product  is  the  number  obtained  by  multiplying;  as, 
8  cents  in  the  above. 

47.  The  Sign  of  multiplication  is  an  oblique  cross  X,  and  is 
read  times  when  the  multiplier  is  placed  first,  and  multiplied  by 
when  the  multiplicand  is  first.     When  placed  between  two  num- 
bers it  shows  that  one  is  to  be  multiplied  by  the  other.     4X2 
cents  is  read  4  times  2  cents  and  means  that  2  cents  are  taken  4 
times  in  addition,  or  that  2  cents  are  multiplied  by  4. 

The  multiplicand  and  multiplier  are  called  factors,  as  they 
both  together  produce  the  product.  The  multiplicand  may  be 
either  an  abstract  or  a  concrete  number.  The  multiplier  must 
always  be  an  abstract  number.  The  product  is  an  abstract  or 
concrete  number  according  as  the  multiplicand  is  abstract  or 
concrete. 

Multiplication  is  a  short  method,  of  performing  addition  when 
the  numbers  to  be  added  are  equal. 

MULTIPLICATION    TABLE 


1X1=1 

2X1=2 

3X1=3 

4X1=4 

1X2=2 

2X2=4 

3X2=6 

4X2=8 

1X3=3 

2X3=6 

3X3=9 

4  X    3  =  12 

1X4=4 

2X4=8 

3  X     4  =  12 

4  X     4  =  16 

1X5=5 

2  X     5  =  10 

3  X     5  =  15 

4  X     5  =  20 

1X6=6 

2  x     6  =  12 

3  X     6  =  18 

4  X     6  =  24 

1X7=7 

2  X     7  =  14 

3  X     7  =  21 

4  X     7  =  28 

1X8=8 

2  X    8  =  16 

3  X     8  =  24 

4  X     8  =  32 

1X9=9 

2  X     9  =  18 

3  X     9  =  27 

4  X     9  =  36 

1  X  10  =  10 

2  X  10  =  20 

3  X  10  =  30 

4  X  10  =  40 

1  X  11  =  11 

2  X  11  =  22 

3  X  11  =  33' 

4  X  11  =  44 

1  X  12  =  12 

2  X  12  =  24 

3  X  12  =  36 

4  X  12  =  48 

22 


MULTIPLICATION 


23 


5X1=5 

6X1=6 

7X1=7 

8  X  1=8 

5  X  2  =  10 

6  X  2  =  12 

7  x  2  =  14: 

8  X  2  =  16 

5  X  3  =  15 

6  X  3  =  18 

7  X  3  =  21 

8  X  3  =  24 

5  X  4  =  20 

6  X  4  =  24 

7  X  4  =  28 

8  X  4  =  32 

5  X  5  =  25 

6  X  5  =  30 

7  X  5  =  35 

8  X  5  =  40 

5  X  6  =  30 

6  X  6  =  36 

7  X  6  =  42 

8  X  6  =  48 

5X  7  =  35 

6  X  7  ==  42 

7  X  7  =  49 

8  X  7  =  56 

5  x  8  =  40 

6  X  8  =  48 

7  X  8  =  56 

8  X  8  =  64 

5  x  9  =  45 

6  X  9  =  54 

7  X  9  =  63 

8  X  9  =  72 

5  X  10  =  50 

6  X  10  =  60 

7  X  10  =  70 

8  X  10  =  80 

5  X  11  =  55 

6  X  11  =  66 

7  X  11  =  77 

8  X  11  =  88 

5  X  12  =  60 

6  x  12  =  72 

7  X  12  =  84 

8  X  12  =  96 

9X1=   9 

10  X  1  =  10 

11  X  1=  11 

12  X  1  =  12 

9  X  2  =  18 

10  X  2=  20 

11  X  2=  22 

12  X  2  =  24 

9  X  3  =  27 

10  X  3  =  30 

11  X  3=  33 

12  X  3=  36 

9  x  4  =  36 

10  X  4  =  40 

11  X  4  =  44 

12  X  4=  48 

9  X  5  =  45 

10  X  5  =  50 

11  X  5=  55 

12  X  5=  60 

9  X  6  =  54 

10  X  6  ==  60 

11  X  6=  66 

12  X  6  =  72 

9  X  7  =  63 

10  X  7  =  70 

11  X  7=  77 

12  X  7  =  84 

9  X  8  =  72 

10  X  8=  80 

11  X  8  =  88 

12  X  8  =  96 

9  x  9  =  81 

10  X  9  =  90 

11  X  9  =  99 

12  X  9  =  108 

9  X  10  =  90 

10  X  10  =  100 

11  x  10  =  110 

12  X  10  =  120 

9  X  11  =  99 

10  x  11  =  110 

11  X  11  =  121 

12  X  11  =  132 

9  X  12  =  108 

10  X  12  =  120 

11  x  12  =  132 

12  X  12  =  144 

48.  When  the  multiplier  consists  of  one  figure. 

1.  Multiply  436  by  4. 

EXPLANATION. — 4  times  6  units  are  24 
units,  or  2  tens  and  4  units;  write  the  4 
units  in  units'  place,  and  add  the  2  tens  to 
the  product  of  tens.  4  times  3  tens  are  12 
tens,  plus  the  2  tens  (from  the  product  of 
units)  are  14  tens,  or  1  hundred  and  4  tens; 
write  the  4  tens  in  tens'  place  and  add  the  1 


MULTIPLICAND 

MULTIPLIER 

PRODUCT 


SOLUTION 
436 

4 
1744 


hundred  to  the  product  of  hundreds.    4  times  4  hundreds  are  16  hundreds, 
plus  the  1  one  hundred  are  17  hundreds,  or  1  thousand  and  7  hundreds; 
write  the  7  hundred  in  hundreds'  place,  and  the  1  thousand  in  thousands' 
place.    The  result,  1744,  is  the  product  required. 
Find  the  product  of  each  of  the  following : 

(2)  (3)  (4)  (5)  (6)  (7) 

1624         2436         1837         3262         8425         2987 
234567 


24 


NEW   BUSINESS   ARITHMETIC 


(8)     (9)     (10)    (11)    (12) 

3204    4624    3285    4623    8423 

89465 


6327 

7 


14.  Multiply  12687  by  2.         IS.  Multiply  32346  by  6. 

15.  Multiply  43745  by  3.         19.  Multiply  49728  by  7. 

16.  Multiply  81968  by  4.         20.  Multiply  27856  by  8. 

17.  Multiply  32643  by  5.         21.  Multiply  38769  by  9. 

22.  In  1  gallon  there  are  4  quarts.     How  many  quarts  are 
there  in  2647  gallons? 

23.  A  man  receives  $2645  a  year.     How  much  does  he  receive 
in  5  years? 

24.  What  will  it  cost  to  dig  a  ditch  7  miles  long  at  $273  per 
mile? 

25.  What  will  8  acres  of  land  cost  at  $259  per  acre  ? 

26.  When  flour  is  selling  at  $9  per  barrel,  what  will  3642  bar- 
rels cost? 

27.  If  a  man  walks  6  miles  an  hour,  how  many  miles  will  he 
walk  in  16  days  by  traveling  8  hours  each  day? 

28.  If  a  bank  clears  $37293  each  year,  how  much  will  it  clear 
in  7  years? 

49.    When    the   multiplier   is   expressed   by   more    than    one 
figure. 

1.  Multiply  436  by  243. 


MULTIPLICAND 
MULTIPLIER 


PARTIAL 
PRODUCTS 


PRODUCT 


SOLUTION 

436 
243 


1308 
1744 
872 
105948 


EXPLANATION. — The  product  of  436  by  3 
units  is  1308  units;  write  so  the  right-hand 
figure  is  in  units'  place.  The  product  436  by  4 
tens  is  1744  tens;  write  so  the  right-hand  fig- 
ure is  in  tens'  place.  The  product  of  436  by 
2  hundreds  is  872  hundreds;  write  so  the 
right-hand  figure  is  in  hundreds'  place.  Add 
the  partial  products.  This  gives  105948,  the 
product  required. 


1.  When  the  multiplier  contains  two  or  more  figures,  the  several  re- 
sults obtained  by  multiplying  by  each  figure  are  called  partial  products. 

2.  When  there  are  ciphers  between  the  significant  figures  of  the  mul- 
tiplier, pass  over  them,  and  multiply  by  the  significant  figures  only. 


MULTIPLICATION  25 

From  the  preceding  examples  and  illustrations  we  deduce  the 
following : 

To  Multiply  Whole  Numbers 

a.  When  the  multiplier  contains  two  or  more  figures,  write  it 
under  the  multiplicand  so  that  figures  of  the  same  order  are  in  the 
same  column. 

b.  Begin  at  the  right  and  multiply  the  multiplicand  by  each 
figure  of  the  multiplier,  and  write  the  first  figure  of  each  product 
under  the  figure  of  the  multiplier  that  produced  it. 

c.  Add  the  partial  products. 

NOTES. — 1.  When  there  are  ciphers  at  the  right  of  the  multiplier  or 
multiplicand,  place  the  right-hand  figure  of  the  multiplier  under  the  right- 
hand  figure  of  the  multiplicand  and  multiply  as  if  there  were  no  ciphers. 

2.  After  multiplying  annex  to  the  product  as  many  ciphers  as  there 
are  at  the  right  of  both  the  multiplier  and  multiplicand. 

>V9,    P3SS 

PROBLEMS 

(2)         (3)         (4)         (5)         (6)          (7) 
Multiply     365         463         268         796         397         1584 
by  47  36  52  68         286  674 

8.  Multiply    368  by      43.         12.  Multiply    8765  by    574. 

9.  Multiply  4096  by    246.         13.  Multiply    3700  by  1420. 

10.  Multiply  1628  by    250.         U.  Multiply  12000  by    900. 

11.  Multiply  2374  by  2300.         15.  Multiply    7324  by  2364. 

16.  At  $436  per  acre,  what  will  394  acres  cost? 

17.  Find  the  cost  of  368  hogsheads  of  tobacco  at  $567  per 
hogshead. 

18.  A  drover  bought  763  head  of  oxen  at  an  average  of  $67 
per  head.     What  did  they  cost  him? 

19.  How  many  feet  are  there  in  150  miles,  if  there  are  5280 
feet  in  1  mile? 

20.  In  1  pound  there  are  7000  grains.     How  many  grains  are 
there  in  1260  pounds? 

21.  A  factory  employs  236  men  at  an  average  of  $147  per 
month.     What  amount  do  they  all  receive? 


26  NEW  BUSINESS  ARITHMETIC 

22.  A  manufacturer   sold   328   self-binding   reapers   at  $469 
each.     How  much  did  he  receive  for  them  ? 

23.  If  1  barrel  of  flour  weighs  200  pounds,  what  will  760 
barrels  weigh? 

24.  What  will  894  bushels  of  wheat  weigh  if  1  bushel  weighs 
60  pounds? 

25.  A   farmer  bought  207   acres   of  land  at   $80   per  acre. 
What  was  the  cost? 

26.  In  1  hogshead  there  are  63  gallons.     How  many  gallons 
are  there  in  3267  hogsheads? 

27.  How  many  cubic  inches  are  there  in  2362  gallons,  if  1 
gallon  contains  231  cubic  inches? 

28.  If  in  1  bushel  of  apples  there  are  56  pounds,  how  many 
pounds  are  there  in  942  bushels  ? 

29.  Find  the  cost  of  2450  bushels  of  wheat  at  85  cents  per 
bushel. 

80.  If  a  man  takes  30300  steps  each  day  for  260  days,  how 
many  steps  does  he  take? 

81.  If  a  boy  writes  1605  words  an  hour,  how  many  words 
will  he  write  in  40  days  by  working  12  hours  each  day? 

82.  A  man  bought  420  loads  of  corn,  36  bushels  in  each  load. 
How  many  pounds  did  he  buy  if  each  bushel  weighs  56  pounds? 

88.  I  sold  18  carloads  of  hogs,  35  hogs  in  each  car,  at  10 
cents  per  pound.  The  hogs  averaged  320  pounds.  How  much 
did  I  receive  for  the  whole  lot? 

SPECIAL  CASES  IN  MULTIPLICATION 

a.  To  multiply  by  10,  100  or  1  with  any  number  of  ciphers 
following. 

b.  To  multiply  when  the  multiplier  has  ciphers  at  the  right. 

c.  To  multiply  when  there  are  ciphers  at  the  right  of  each 
term. 

d.  To  multiply  when  the  unit  figure  of  the  multiplier  is  one. 

e.  To  multiply  when  the  left-hand  figure  of  the  multiplier  is 
one. 

f.  To  multiply  by  11,  22,  etc. 

g.  Cross  multiplication. 


MULTIPLICATION  27 

Illustration 

a.  32  X  100  =  32  and  the  addition  of  two  ciphers,  or  3200. 
EXAMPLES.— 49  X  100 ;  53  X  10 ;  645  X  10 ;  327  X  100. 

b.  24  X  90  =  9  X  24  and  the  addition  of  one  cipher,  or  2160. 
EXAMPLES.— 25  X  80 ;  84  X  600;  36  X  200;  71  X  800. 

c.  90  X  80  =  9  X  8  and  the  addition  of  two  ciphers,  or  7200. 
EXAMPLES.— 240  X   30;  3600   X  900;  2500  X  2500;  90   X 

910. 

d.  243  X  21  ==      243  X  21 

486 


5103 

EXAMPLES.— 294  X  31 ;  846  X  51 ;  327  X  601 ;  426  X  701. 

e.  374  X  16  =       374  X   16 

2244 
5984 
EXAMPLES.— 427  X  17;  375  X  104;  724  X  19 ;  562  X  109. 

f.  3452  X  11  =  37972. 

Write  2  as  the  first  figure,  (5  +  2)  as  the  second,  (5  +  4)  as 
the  third,  (3  +  4)  as  the  fourth  and  3  as  the  fifth.  Carry  when 
necessary. 

To  multiply  by  33,  multiply  each  addition  by  3,  then  add  the 
carrying  number. 

EXAMPLES.— 3463  X  11;  4234  X  22;  3714  X  33;  4637  X  55; 
9876  X  11;  7964  X  66. 

gm  64  X  76  =  4864. 

(6X4)  =  units.  Write  the  4  and  carry  the  2.  2  4 
(6X6)  +  (4X7)  =  tens'  place.  Write  the  6  and  carry  the 
6  +  (6  X  ?)  =  hundreds'  place;  4864  the  desired  result. 

EXAMPLES. — 

1.  24  X  36  =  x  2.  94  X  63  =  x 

62  X  47  —  x  38  X  45  =  x 

74  X  39  =_£  57  X  67  =_£ 

x  x 


28  NEW    BUSINESS   ARITHMETIC 

PROBLEMS  IN    ADDITION,  SUBTRACTION  AND 
MULTIPLICATION 

50.   1.  Bought  230  bushels  of  corn  at  40  cents  a  bushel  and 
365  bushels  of  wheat  at  80  cents  a  bushel.     What  did  both  cost? 

2.  A  teacher  receives  a  salary  of  $1300  a  year  and  pays  $360 
for  board,  $200  for  clothing,  $100  for  books  and  $45  for  other 
expenses.     What  does  he  save  in  the  year? 

3.  A  merchant  bought  288  barrels  of  flour  for  $1960  and  sold 
it  at  $8  a  barrel.     How  much  did  he  gain  ? 

4.  A  farmer  bought  34  head  of  cattle  at  $18  a  head  and  sold 
them  at  $21  a  head.     How  much  did  he  gain  by  the  operation? 

5.  A  lawyer  has  an  income  of  $4325  a  year,  and  his  daily 
expenses  are  $4.     What  will  he  save  in  a  year  of  365  days? 

6.  A  sold  a  farm  of  360  acres  at  $45  an  acre;  B  sold  one  of 
280  acres  at  $60  an  acre.     Which  received  the  greater  sum,  and 
how  much? 

7.  A  farmer  sold  263  bushels  of  wheat  at  $1  a  bushel.     He 
received  in  payment  23  yards  of  cloth  at  $4  a  yard,  and  the  bal- 
ance in  groceries.     What  did)  the  groceries  cost  him  ? 

8.  I  sold  17  cows  at  $36  apiece  and  for  them  received  65  tons 
of  hay  at  $9  a  ton  and  the  remainder  in  money.     How  much 
money  did  I  receive? 

9.  A  man  bought  a  house  for  $2867.     He  expended  in  repair- 
ing it  $16  for  plumbing,  $73  for  carpenter  work,  $48  for  painting. 
He  then  sold  the  house  for  $3265.     What  did  he  gain  ? 

10.  Two  persons  start  from  the  same  point  and  travel  in  oppo- 
site directions,  one  at  the  rate  of  45  miles  a  day  and  the  other  36 
miles  a  day.     How  far  apart  will  they  be  in  16  days? 

11.  A  dealer  bought  535  barrels  of  pork  at  $8  a  barrel.     He 
sold  245  barrels  of  it  at  $10  a  barrel  and  the  remainder  at  $7  a 
barrel.     What  did  he  gain  or  lose? 

12.  Mr.  Brown  has  an  income  of  $12650  a  year.     He  spends 
$1650  for  house  rent  and  twice  as  much  for  other  expenses.  How 
much  does  he  save  in  a  year? 


MULTIPLICATION  29 

IS.  A  sold  3  houses.  For  the  first  he  received  $2875,  for  the 
second  $230  more  than  the  first,  and  for  the  third  as  much  as  the 
first  two.  How  much  did  he  receive  for  all? 

14.  Mr.  C  bought  14  cows  at  $23  each,  7  horses  at  $96  each, 
34  oxen  at  $57  each,  and  300  sheep  at  $2  each.     He  sold  the 
whole  for  $3842.     What  did  he  gain? 

15.  A  merchant  having  $7632  deposited  in  his  bank,  drew  out 
for  the  purchase  of  dry-goods,   $1867;  groceries,   $362;  boots 
and  shoes,  $218;  hardware,  $160.     What  amount  had  he  left  in 
the  bank? 


DIVISION 

51.  Division  is  finding  how  many  times  one  number  is  con- 
tained in  another. 

52.  The  Dividend  is  the  number  to  be  divided. 

53.  The  Divisor  is  the  number  by  which  to  divide. 

54.  The  Sign  of  division  is  a  short  horizontal  line  with  a 
dot  above  and  one  below  it  -=-.     The  divisor  follows  the  dividend 
as  $6  -^  2  or  $6  -4-  $2.     It  may  be  written  jf^  2)  $6,  or  $6(2, 

2 

55.  The  Quotient  is  the  number  obtained  by  dividing,  and 
shows  how  many  times  the  divisor  is  contained  in  the  dividend. 

1.  When  the  dividend  does  not  contain  the  divisor  an  exact  number  of 
times,  the  part  of  the  dividend  left  is  called  the  remainder,  and  it  must  be 
less  than  the  divisor. 

2.  As  the  remainder  is  always  a  part  of  the  dividend,  it  is  always  of 
the  same  name  and  kind. 

3.  When  there  is  no  remainder,  the  division  is  said  to  be  exact. 

4.  When  the  process  of  dividing  is  performed  mentally,  and  the  re- 
sults only  are  written,  the  operation  is  termed  Short  Division. 

5.  When  the  whole  process  of  division  is  written,  the  operation  is 
termed  Long  Division. 

SHORT  DIVISION 

56.  When  the  divisor  consists  of  one  figure. 
1.  Divide  693  by  3. 

SOLUTION 

DIVISOR  3)693      DIVIDEND 

QUOTIENT   «  231 

Find  the  quotient  of  each  of  the  following: 

m  W  (4)  (5)  (6)  (7) 

2)864         3)936         5)550         2)6248       3)9636       4)4884 

(8)  (9)  (10)  (11)  (12)          (13) 

2)8624       3)9306       4)80480     3)30609     2)20840     5)5055 

80 


DIVISION  31 

14.  Divide  1712  by  8. 

SOLUTION 

8)1712 
214 

Solve  the  following  problems: 

(15)  (16)  (17)  (18)  (19)  (20) 

4)1720       5)3675       6)4992       7)2674       8)9296       9)11916 

21.  At  $9  a  barrel  how  many  barrels  of  flour  can  be  bought 
for  $10926  ? 

22.  How  many  calves  can  I  buy  with  $2940  at  $7  per  head? 

23.  Eight  men  own  22824   sheep.     If  they  have  the   same 
number,  how  many  has  each? 

24.  Five  men  invest  equally  in  business.     The  total  invest- 
ment was  $23770.     How  much  did  each  invest? 

25.  When  broadcloth  was  selling  at  $6  per  yard  I  paid  $97362 
for  an  invoice.     How  many  yards  did  I  buy? 

LONG  DIVISION 

57.  When  the  divisor  is  expressed  by  more  than  one  figure. 
1.  Divide  5848  by  43. 

SOLUTION 

43)5848(136 
43 
154 
129 


258 
258 


From  the  preceding  we  induce  the  following : 
To  Divide  Whole  Numbers 

o.  Write  the  divisor  on  the  left  of  the  dividend. 

b.  Find  how  many  times  the  divisor  is  contained  in  the  least 
number  of  figures  which  will  contain  it  at  the  left  of  the  dividend, 
and  write  the  result  in  the  quotient  at  the  right. 


32  NEW   BUSINESS   ARITHMETIC 

c.  Multiply  this  quotient  figure  by  the  divisor,  subtract  the 
product  from  the  figures  of  the  dividend  used  and  to  the  remain- 
der bring  down  the  next  figure  of  the  dividend,  which  divide  as 
before,  and  so  continue  until  all  the  figures  of  the  dividend  have 
been  brought  down  and  used. 

d.  If,  after  bringing  down  a  figure,  the  divisor  is  too  large  to 
be  contained  in  the  dividend,  ivrite  a  cipher  in  the  quotient  and 
bring  down  the  next  figure  in  the  dividend. 

e.  If  there  is  a  remainder  in  the  quotient  it  should  be  written 
at  the  right  of  the  quotient  with  the  divisor  under  it. 

NOTES. — 1.  If  any  remainder  be  equal  to  or  greater  than  the  divisor,, 
the  quotient  figure  is  too  small,  and  must  be  increased. 

2.  If  the  product  of  the  divisor  by  the  quotient  figure  be  greater  than 
the  dividend,  the  quotient  figure  is  too  large,  and  must  be  diminished. 

PROBLEMS 

2.  Divide  7668  by  36.  6.  Divide  24492  by  78. 

3.  Divide  1666  by  49.  7.  Divide  11808  by  246. 

4.  Divide  3484  by  52.  8.  Divide  49815  by  369. 

5.  Divide  20995  by  85.  9.  Divide  1720  by  5. 

10.  Divide  32740  by  154. 

11.  Divide  32572  by  34. 

12.  Divide  1554768  by  216. 

13.  Divide  93840  by  63.     Remainder  33. 

U.  Divide  10557312  by  32.  15.  Divide  3931476  by  278. 

16.  Divide  352417  by  29.     Remainder  9. 

17.  Divide  75088  by  52.         18.  Divide  1674918  by  189. 

19.  Divide  42647  by  92.     Answer,  463|i. 

20.  Divide  163513  by  497.     21.  Divide  127960  by  267. 
22.  Divide  36928  by  69. 

28.  At  $76  each,  how  many  horses  can  be  bought  for  $9728? 

24.  274  wagons  cost  $29592.     What  was  the  average  price 
per  wagon? 

25.  B  paid  $19872  for  207  acres  of  land.     What  was  the  price 
per  acre? 

26.  A  farmer  raised  9765  bushels  of  wheat  on  223  acres. 
What  was  the  yield  per  acre? 


DIVISION  33 

27.  A  manufacturing  company  made  a  profit  of  $37840  in  215 
days.     What  was  the  daily  profit? 

58.  When  there  are  ciphers  at  the  right  of  the  divisor. 

I.  Divide  34216  by  900. 

EXPLANATION.— Cut    off    the 
ciphers  at  the  right  of  the  di- 

SOLUTION  visor  and  the  same  number  of 

9|00)342|16  figures  from  the  right  of  the 

38  QUOTIENT.  16  REMAINDER  dividend.  Divide  the  remain- 
ing figures  of  the  dividend  by 
the  remaining  figures  of  the 

divisor.     To  the  remainder,   if  any,  annex  the   figures   cut  off   from  the 

dividend. 

PROBLEMS 

2.  Divide  362076  by  60.         3.  Divide  350000  by  14000. 
4.  Divide  28520  by  1500.       5.  Divide  18065  by  1200. 
6.  Divide  1720800  by  3600.  7.  Divide  968050  by  12900. 
8.  Divide  836290  by  1780.     9.  Divide  924000  by  2640. 
10.  Divide  7802030  by  6070. 

II.  At  $150  each,  how  many  horses  can  be  bought  for  $11250? 
12.  A  real  estate  dealer  received  $8640  for  36  lots.     What 

was  the  average  price  of  the  lots  ? 

PROBLEMS  IN  ADDITION,  SUBTRACTION,  MULTIPLICATION 

AND  DIVISION 

59.  1.  A  merchant  owes  $59,  $84,  $36  and  $17.     He  pays 
$42.     How  much  does  he  still  owe? 

2.  A  bought  four  bills  of  goods  amounting  to  $740,   $965, 
$342  and  $196.     He  paid  $1262  on  them.     How  much  does  he 
still  owe  for  the  goods? 

3.  A  laborer  bought  a  coat  worth  $16,  a  vest  worth  $3,  and  a 
pair  of  pants  worth  $5.     How  many  days  had  he  to  work  to  pay 
for  his  suit,  his  services  being  worth  $2  a  day  ? 

L  I  bought  95  bushels  of  wheat  at  78  cents  per  bushel,  and 


34  NEW   BUSINESS   ARITHMETIC 

paid  for  it  in  cloth  at  19  cents  per  yard.     How  many  yards  were 
required  ? 

5.  Four  men  have  $2890.     The  first  has  $610;  the  second 
$593 ;  the  third  $975.     How  much  has  the  fourth  man? 

6.  A  clerk's  income  is  $898  a  year  and  his  expenses  are  $2  a 
day.     How  much  will  he  save  in  two  years  of  365  days  each? 

7.  How  many  pounds  of  cheese  at  9  cents  per  pound  must  be 
given  for  27  pounds  of  tea  worth  80  cents  a  pound  ? 

8.  A  person  sells  15  tons  of  hay  at  $22  per  ton,  and  receives 
in  payment  a  carriage  worth  $125,  a  cow  worth  $45,  a  colt  worth 
$40,  and  the  balance  in  cash.     How  much  money  ought  he  to 
receive  ? 

9.  A  deposited  in  bank  $426,  $743,  $860,  $910,  $85,  $1269 
and  $26.     He  withdrew  from  the  bank  $705,  $210,  $500.     How 
much  had  he  then  in  the  bank  ? 

10.  I  sold  48  horses  at  $86  each,  and  with  the  money  bought 
calves  at  $8  each.     How  many  calves  did  I  buy  ? 

11.  I  bought  two  pieces  of  land,  one  of  360  acres  at  $29  per 
acre,  the  other  of  194  acres  at  $41  per  acre.     What  did  both 
pieces  cost  me? 

12.  A  bought  175  cows  at  $23  each,  and  268  hogs  at  $13  each. 
B  bought  79  cows  at  $34  each,  and  170  hogs  at  $11  each.     How 
much  more  did  A  pay  than  B  ? 

13.  I  bought  a  farm  for  $2165,  paying  $725  cash,  and  the  bal- 
ance in  monthly  payments  of  $120  each.     How  many  monthly 
payments  did  I  make? 

14-  A  teacher  receives  a  salary  of  $75  per  month  for  1  year. 
His  board  cost  $20  per  month,  other  expenses  $180  for  the  year. 
With  the  balance  of  his  money  he  buys  books  at  $6  a  volume. 
How  many  books  can  he  buy  ? 

15.  A  man  bought  26  tons  of  coal  at  $6  per  ton.     For  how 
much  must  he  sell  it  per  ton  to  gain  $52  on  the  26  tons? 

16.  B  had  $9628,  of  which  he  invested  $1860  in  bank  stock, 
$2108  in  horses,  $974  in  hogs,  $1218  in  sheep,  and  the  remainder 
in  land.     What  did  the  land  cost  him? 

17.  A    widow    has    a    farm    valued    at    $6720;    also    three 
houses  worth  $12530,  $11324  and  $9875.     She  has  a  daughter 


DIVISION  35 

and  two  sons.  To  the  daughter  she  gives  one-fourth  the  value 
of  the  farm,  and,  one-third  the  value  of  the  houses,  and  then 
divides  the  remainder  equally  among  the  boys.  How  much  did 
each  receive? 

18.  A  is  worth  $960,  B  is  worth  five  times  as  much  as  A,  less 
$600,  and  C  is  worth  three  times  as  much  as  A  and  B  and  $300 
more.     What  are  B  and  C  each  worth  and  how  much  are  they 
all  worth? 

19.  A  grocer  bought  7  barrels  of  fish  at  $18  per  barrel,  but 
one  barrel  proved  to  be  bad.     This  he  sold  for  $5  less  than  cost, 
and  the  remainder  at  an  advance  of  $3  per  barrel.     Did  he  gain 
or  lose,  and  how  much? 

20.  If  a  clerk's  salary  is  $600  a  year  and  his  personal  expenses 
$320,  how  many  years  before  he  will  be  worth  $6600  if  he  has 
$1000  at  the  present  time? 

21.  A  man  went  into  business  with  a  capital  of  $1500;  the 
first  year  he  gained  $800,  the  second  year  $950,  the  third  year 
$700,  and  the  fourth  year  $625,  when  he  invested  the  whole  in  a 
cargo  of  tea  and  doubled  his  money.     What  was  he  then  worth  ? 

22.  A  butcher  bought  9  calves  for  $54,  and  8  lambs  for  $16. 
How  much  more  did  he  pay  for  a  calf  than  a  lamb? 

28.  A  farmer  sold  to  a  grocer  380  pounds  of  pork,  at  7  cents 
per  pound ;  150  pounds  of  butter,  at  17  cents  per  pound,  and  one 
cheese  weighing  53  pounds,  at  9  cents  per  pound,  and  received 
in  payment  22  pounds  of  sugar,  at  the  rate  of  11  pounds  for  a 
dollar;  225  pounds  of  flour  at  4  cents  per  pound;  15  pounds  of 
tea,  at  65  cents  per  pound;  one  half-barrel  of  fish,  at  $18  per 
barrel,  and  one  set  of  dishes  worth  $27.  Did  the  farmer  owe  the 
grocer,  or  the  grocer  the  farmer,  and  how  much  ? 

24.  A  speculator  bought  200  bushels  of  apples  for  $90,  and 
sold  the  same  for  $120.     How  much  did  he  make  per  bushel  ? 

25.  A  milkman  sold  120  quarts  of  milk,  at  5  cents  per  quart, 
and  took  in  payment  one  pig  worth  $1.50,  and  the  balance  in 
sheeting,  at  10  cents  per  yard.     How  many  yards  did  he  receive? 

26.  A  manufacturing  company  made  928  yards  of  cloth  on 
Monday,  1142  yards  on  Tuesday,  1468  on  Wednesday  and  876 


36  NEW   BUSINESS    ARITHMETIC 

yards  on  Thursday,  and  sold  1940  yards  of  it.     How  many  yards 
remained  ? 

21.  A  man  bought  a  farm,  paying  $1690  down.  After  mak- 
ing three  other  payments  of  $945,  $765  and  $2740,  the  amount 
unpaid  was  $3628.  He  sold  the  farm  for  $8278.  What  was  his 
loss? 

28.  A  merchant's  store  was  insured  for  $21650,  and  his  goods 
for  $17645.     The  store  was  valued  at  $25000,  and  the  goods  at 
•$22564.     Both  were  destroyed  by  fire.     What  was  his  loss  ? 

29.  A,  B,  C  and  D  formed  a  partnership.     A  invested  $720 
more  than  B ;  C  invested  $1280  less  than  B,  and  D  invested  $945 
less  than  A  and  C  together.     What  was  the  total  investment  if 
B  invested  $2450? 

30.  A  speculator  bought  200  acres  of  land  at  $45  per  acre, 
and  afterwards  sold  150  acres  of  it  for  $11550;  the  balance  he 
sold  at  a  gain  of  $5  per  acre,  and  received  in  payment  $250  cash, 
and  the  balance  in  sheep  at  $5  each.     How  many  sheep  did  he  re- 
ceive ?    What  was  his  profit  on  the   land  ? 


FACTORING 

60.  An  Exact  Divisor  of  a  number  is  a  number  that  will 
be  contained  in  it  an  integral  number  of  times. 

61.  A  Factor  of  a  number  is  an  integral  divisor  of  the  num- 
ber.   The  factors  of  18  are  2,  3  and  3 ;  of  30  are  2,  3  and  5. 

62.  A  Prime  Number  is  one  which  cannot  be  divided  or 
separated  into  factors,  except  1  and  that  number;  as  3,  5,  7,  11 
and  13. 

63.  A  Composite  Number  is  one  which  can  be  resolved  or' 
separated  into  integral  factors ;  as  4,  6,  9,  10  and  12. 

64.  An  Even  Number  is  one  that  is  exactly  divisible  by  2 ;  as 
8,  16,  24  and  30. 

65.  An  Odd  Number  is  one  that  is  not  exactly  divisible  by  2; 
as  5,  9,  7,  15  and  21. 

66.  A  Prime  Factor  is  one  that  is  a  prime  number ;  as  3,  11, 
J7  and  23. 

67.  Factoring  is  finding  the  factors  of  a  number. 
1.  What  are  the  prime  factors  of  42? 

SOLUTION 

2)42 
3)21 

7 

From  the  preceding  definitions  and  example  we  have  the  fol- 
lowing : 

To  Separate  a  Number  Into  Its  Prime  Factors 

a.  Divide  the  given  number  by  any  prime  factor. 

b.  Divide  the  quotient,  if  a  composite  number,  by  any  prime' 
factor  and  so  continue  dividing  until  the  quotient  is  a  prime- 
number. 

c.  The  divisors  and  the  last  quotient  are  the  prime  factors* 

37 


38  NEW   BUSINESS   ARITHMETIC 

Find  the  prime  factors  of  the  following  numbers : 

2.  9  11.  108     20.   300  29.  1347 

8.  12  12.  120     21.   385  80.  2898 

4.  18  13.  124     #&   465  81.  4292 

5.  36  14.  186     28.   525  5£.  9222 

6.  35  15.  225     #4.   644  33.  8151 

7.  42  16.  231     £5.   656  54.  3476 

8.  50  17.  288     26.   756  55.  5270 
P.  66  18.  294     07.  1273  36.  8892 

10.  96  IP.  297     28.  2920  57.  13717 


CANCELLATION 

68.,  Since  dividing  both  dividend  and  divisor  by  the  same 
number  does  not  change  the  quotient,  we  may  strike  out  or  re- 
ject equal  factors  from  both  dividend  and  divisor  without  affect- 
ing the  result. 

69.  Cancellation   is    striking   out   equal    factors    from   both 
dividend  and  divisor.     Cancellation  is  a  short  method  of  division-. 

70.  The  Sign  of  cancellation  is  an  oblique  line,   /;   when 
drawn  across  a  number,  it  shows  the  number  has  been  cancelled  ; 
as,  £,  fy,  §  and  $. 

The  most  common  method  is  to  write  the  dividend  above  a  horizontal 
line  and  the  divisor  beneath  it,  although  a  vertical  line  with  the  divisor 
on  the  left  and  the  dividend  on  the  right  is  sometimes  used. 

If  the  dividend  or  divisor  is  a  composite  number  it  should  first  be  re- 
solved into  its  prime  factors,  before  beginning  the  operation  of  cancella- 
tion. 

1.  Divide  4X8X3X5X7  by  2X3X4X5. 

EXPLANATION. — Strike  out  the  fac- 
tors 3,  4  and  5  from  both  dividend 

SOLUHUJ*  ...  _,.  _.         ,          ,.. 

4  and  divisor.     Since  2  in  the  divisor 

ity&V^y^y?  *s  a  fact°r  °f  8  in  the  dividend,  we 

cancel   these,    leaving   the    factors   4 


*v  ' 

f  X  P  X  f>  times  7  in  the  dividend,  or  28,  the 

quotient. 


CANCELLATION  39 

We  therefore  have  the  following: 

To  Find  a  Quotient  by  Cancellation 

a.  Write  the  numbers  composing  the  dividend  above  a  hori- 
zontal line  and  those  composing  the  divisor  below  it. 

b~  Cancel  all  factors  common  to  both  dividend  and  divisor. 

c.  Multiply  the  remaining  factors  of  the  upper  numbers  or 
dividend  together,  and  the  remaining  factors,  if  any,  of  the  lower 
numbers  or  divisor  together.  Divide  the  upper  product  by  the 
lower  and  the  result  will  be  the  quotient  desired. 

NOTES. — 1.  Rejecting  a  factor  from  any  number  is  dividing  the  num- 
ber by  that  factor. 

2.  When  a   factor  is  cancelled,  the  unit,  1,  is  supposed  to  take   its 
place. 

3.  One  factor  in  the  dividend  will  cancel  only  one  equal  factor  in  the 
divisor. 

4.  If  all  the  factors  or  numbers  of  the  divisor  are  cancelled,  the  prod- 
uct of  the  remaining  factors  of  the  dividend  will  be  the  quotient. 

5.  By  many  it  is  thought  more  convenient  to  write  the  factors  of  the 
dividend  on  the  right  of  a  vertical  line,  and  the  factors  of  the  division  on 
the  left. 

Solve  the  following  problems  by  cancellation : 

2.  Divide  3X7X4X5X11  by  5X7X4X3. 

3.  Divide  2X4X6X8X  10  by  2X4X5X6. 

4.  Divide  8X6X  12  X  15  by  5X3X4X2X3. 

5.  Divide  9  X  8  X  6  X  18  by  2  X  3  X  4  X  3  X  3. 

6.  Divide  7  X  6  X  3  X  1*  by  2  X  3  X  2  X  7. 

7.  Divide  4  X  6  X  12  X  15  XS  by  2X3X6X5X4. 

8.  Divide  3X6X9X  12  X  24  by  3X4X6X8X5. 

9.  How  many  yards  of  calico  at  $.08  per  yard  will  pay  for  14 
bushels  of  turnips  at  $.28  per  bushel? 

10.  If  8  yards  of  cloth  cost  $32,  what  will  19  yards  cost? 

11.  How  many  hogs  at  $9  each  will  pay  for  36  barrels  of 
flour  at  $6  each  ? 

12.  I  exchanged  48  dozen  of  eggs  at  10  cents  per  dozen  for 
sugar  at  8  cents  per  pound.     How  many  pounds  did  I  get? 

13.  I  bought  8  boxes  of  boots,  each  containing  9  dozen  pairs 
at  $18  per  dozen,  and  gave  in  payment  12  loads  of  wheat  of  54 
bushels  each.     What  did  I  receive  per  bushel  for  the  wheat  ? 


40  NEW   BUSINESS  ARITHMETIC 

14.  A  cubic  yard  is  3  feet  deep,  3  feet  long  and  3  feet  wide. 
How  many  cubic  yards  in  24  feet  long,  18  feet  wide  and  6  feet 
deep?  

GREATEST  COMMON  DIVISOR 

71.  A  Common  Divisor  of  two  or  more  numbers  is  a  number 
that  will  divide  them  integrally. 

72.  The  Greatest  Common  Divisor  of  two  or  more  numbers 
is  the  greatest  number  that  will  divide  them  integrally,  or  is  the 
product  of  all  their  common  prime  factors. 

Numbers  are  said  to  be  prime  to  each  other  when  they  have  no 
common  divisor. 

If  a  number  divides  two  or  more  others,  it  will  also  divide 
their  sum  and  difference,  and  also  the  sum  and  difference  of  any 
product  of  them,  because  it  divides  them  when  they  are  taken 
separately.  Hence  if  one  number  divide  the  whole  of  another 
number,  and  also  one  part  of  it,  it  will  divide  the  other  part  also. 
Thus,  9  divides  45  and  27,  and  also  their  difference,  18. 

1.  Find  the  Greatest  Common  Divisor  of  84  and  203. 

EXPLANATION.— Write    the    smaller   number 

SOLUT  as  the  divisor  and  the  larger  as  the  dividend. 

84)203(2  We  know  that  the  G.   C.  D.,  whatever  it  is, 

168  must  divide  84,  and  if  it  divides  84  it  will  also 

35)84(2  divide  twice  that  number  or  168.     If  it  divides 

70  203  and  168  it  must  divide  their  difference,  35, 

~7T\oK/9  according  to  the  principle   laid   down   above. 

Repeating  this  argument  until  the  end,  it  must 

_~§.  divide  7  and  14,  and  as  7  is  contained  in  14 

7)14(2      without  a  remainder,  7  is  the  largest  number 

14  that  will  divide  itself  and  14,  and  hence  is  the 

G.  C.  D. 

From  the  preceding  principles  and  explanations  we  have  the 
following  rule: 

To  Find  the  Greatest  Common  Divisor 

a.  Divide  the  greater  number  by  the  less,  and  then  the  less  by 
the  remainder 'f  until  nothing  is  left. 

b.  The  last  divisor  will  be  the  Greatest  Common  Divisor. 


LEAST    COMMON  MULTIPLE  41 

NOTE.— 1.  If  it  is  desired  to  find  the  G.  C.  D.  of  more  than  two  num- 
bers, first  find  the  G.  C.  D.  of  two  of  them,  and  then  find  the  G.  C.  D.  of 
that  and  another,  and  so  on. 

2.  Find  the  greatest  common  divisor  of  247  and  323. 

3.  Find  the  greatest  common  divisor  of  316  and  664. 

4.  What  is  the  greatest  common  divisor  of  532  and  1274? 

5.  What  is  the  greatest  common  divisor  of  741  and  1273  ? 

6.  What  is  the  greatest  common  divisor  of  1313  and  4108? 

7.  What  is  the  greatest  common  divisor  of  468  and  1266  ? 

8.  What  is  the  greatest  common  divisor  of  224,  280  and  336  ? 

9.  I  have  four  rooms,  respectively  16,  20,  24  and  32  feet  wide. 
How  wide  must  carpet  be  that  will  just  fit  each  room? 

10.  The  sides  of  a  lot  are  112,  126,  140  and  168  feet.     What 
is  the  greatest  length  of  boards  that  can  be  used  in  fencing  it 
without  cutting  them? 

11.  A   farmer  has   four  pieces  of  land.     The  first  has   240 
acres ;  the  second,  180  acres ;  the  third,  300  acres ;  the  fourth,  360- 
acres.     He  wishes  to  divide  them  into  the  largest  possible  fields 
of  equal  side.    How  many  acres  will  there  be  in  each  field? 


LEAST   COMMON  MULTIPLE 

73.  A  Multiple  of  a  number  is  any  number  that  will  integrally 
contain  it.     Thus,  18,  24  and  30  are  multiples  of  6. 

74.  A  Common  Multiple  of  two  or  more  numbers  is  any  num- 
ber that  will  integrally  contain  each  of  them.    Thus,  24  is  a  com- 
mon multiple  of  2,  4,  6  and  8. 

75.  The  Least  Common  Multiple  of  two  or  more  numbers  is 
the  least  number  that  will  integrally  contain  each  of  them.    Thus, 
36  is  the  least  common  multiple  of  6,  12  and  18. 

76.  The  Least  Common  Multiple  contains  all  the  prime  fac- 
tors of  each  of  the  given  numbers. 

It  is  plain  that  the  least  common  multiple  of  numbers  that 
have  no  common  factor  is  the  product.  But  if  the  numbers, 
have  a  common  factor,  that  factor  is  to  be  taken  only  once  unless 


42  NEW   BUSINESS   ARITHMETIC 

it  is  repeated  in  any  of  the  numbers,  in  which  case  it  must  be 
used  as  many  times  as  a  factor  of  the  multiple,  as  the  greatest 
number  of  times  it  appears  in  any  of  the  given  numbers. 

1.  Find  the  least  common  multiple  of  4,  6,  9  and  12. 

EXPLANATION.— Write    the    numbers    in    a 

SOLUTION  horizontal  line.     Since  2  is  a  factor  of  some  of 

2)4,  6,  9,  12  the  numbers,  we  know  that  it  must  be  a  fac- 

2)2,  3,  9,  6  tor  °f  t*16  L.  C.  M.,  hence  we  divide  as  many 

ON-,    o   Q   o'  numbers  as  possible  by  2  and  bring  down  the 

—  quotients   and  undivided  numbers  below.     By 

inspection  we  see  that  2  is  again  a  factor  of 

2  X  2  X  3  X  3  =  36  L.  C.  M.      some  Of  the  numbers  brought  down,  and  hence 

another  2  must  be  a  factor  of  the  L.  C.  M. 

We  therefore  divide  by  2  and  bring  down  the  quotients  and  undivided 
numbers  again.  We  next  divide  by  3  for  a  like  reason  and  bring  down  as 
before.  We  now  have  but  3  left,  and  as  we  would  gain  nothing  by 
dividing  it  by  itself,  we  multiply  together  the  several  divisors  and  last 
quotient,  and  the  result  is  the  L.  C.  M.  sought. 

Suggestion. — The  L.  C.  M.  of  12,  9,  6  and  4  cannot  be  less 
than  12 ;  12  contains  all  of  the  factors  of  itself,  6  and  4  and  3,  one 
of  the  factors  of  9.  It  therefore  remains  to  multiply  the  remain- 
ing factors  12  and  3  to  find  the  L.  C.  M.,  which  is  36. 

From  this  example  we  derive  the  following  rule : 
To  Find  The  Least  Common  Multiple 

a.  Write  the  numbers  in  a  horizontal  line. 

b.  Divide  by  any  prime  number  that  will  exactly  divide  one  or 
more  of  the  given  numbers,  and  write  the  quotients  and  undivided 
numbers  beneath.     Continue  to  divide  until  no  number  will  divide 
more  than  one  of  the  quotients. 

c.  Multiply  the  several  divisors  and  the  last  quotient  together 
and  the  result  will  be  the  L.  C.  M. 

2.  What  is  the  least  common  multiple  of  27,  45,  63  and  81  ? 

3.  What  is  the  least  common  multiple  of  10,  12,  14,  16  and  18? 
Find  the  L.  C.  M.  of  the  following: 

4.  32;  48,  64  and  80.  7.  3,  6,  9,  12,  15,  21  and  24. 

5.  18,  30,  42  and  60.  8.  30,  40,  50,  60,  70  and  80. 

6.  32,  48,  72  and  96.  9.  7,  14,  28,  56,  112  and  224. 


LEAST    COMMON    MULTIPLE  43 

10.  What  is  the  smallest  piece  of  land  that  can  be  divided 
into  fields  of  16,  24  or  30  acres  each? 

11.  What  is  the  least  amount  of  money  with  which  you  can 
purchase  chickens  at  12  cents  each,  ducks  at  20  cents  each,  tur- 
keys at  60  cents  each  or  geese  at  75  cents  each? 

12.  How  many  bushels  will  a  bin  contain  from  which  9,  18  or 
30  bushels  can  be  taken  an  even  number  of  times  ? 

IS.  A  can  shear  42  sheep  in  a  day,  B  63,  and  C  54.  What  is 
the  number  of  sheep  in  the  smallest  flock  that  would  furnish 
exact  days'  labor  for  each  of  them  shearing  alone  ? 


FRACTIONS 

77.  A  Fraction  is  one  or  more  of  the  equal  parts  of  a  unit. 

78.  A  Fractional  Unit  is  one  of  the  equal  parts  of  a  unit,  as, 
one-third,  one-fourth,  one-seventh. 

79.  A  Fraction  is  one  or  more  fractional  units,  as,  one-half, 
three-fourths,  seven-ninths. 

80.  The  Unit  of  a  Fraction  is  the  thing  divided.     The  unit  of 
the  fraction  two-thirds  of  a  dollar,  is  $1 ;  of  four-fifths  is  1 ;  of 
six-elevenths  of  a  bushel  is  1  bushel. 

81.  A  Fraction  is  expressed  by  writing  one  number  above 
and  another  below  a  short  horizontal  line ;  as,  one-fifth,  J ;  three- 
fourths,  j. 

82.  The  Terms  of  a  fraction  are  the  two  numbers  used  to 
express  it. 

83.  The  Denominator  shows  the  number  of  parts  into  which 
the  unit  is  divided  and  is  written  below  the  line. 

84.  The  Numerator  shows  the  number  of  parts  (fractional 
units)  taken,  and  is  written  above  the  line. 

In  £  bushels,  5  is  the  denominator  and  shows  the  unit  (1 
bushel)  is  divided  into  5  equal  parts;  4  is  the  numerator  and 
shows  that  4  of  the  5  equal  parts  are  taken.  £  is  the  fractional 
unit. 

85.  A  Fraction  is  read  by  naming  the  number  and  kind  of 
fractional  units;  as,  f,  three-fifths;  $|,  two-sevenths  of  a  dollar; 
£$  bushel,  nine-twentieths  of  a  bushel. 

Read  the  following  fractions : 


1. 

i- 

4. 

TV 

7. 

TV- 

10. 

2. 

1. 

5. 

A. 

8. 

TV 

11. 

8. 

i. 

6. 

A 

9. 

if. 

12. 

44 

FRACTIONS  45 

Write  the  following  in  the  form  of  fractions : 

13.  Three-fifths.  19.  Twelve-fourteenths. 

14.  Six-sevenths.  20.  Sixteen-twentieths. 

15.  Seven-elevenths.  21.  Eight  twenty-sixths. 

16.  Ten  forty-sevenths.  22.  Thirty- four  seventy-fifths. 

17.  Forty-one   sixtieths.  23.  Sixty-nine    eighty-ninths. 

18.  Fifty-six  seventy-firsts.  24-  Ninety-three    ninety-sixths. 

86.  A  Proper  Fraction  is  one  whose  numerator  is  less  than 
its  denominator;  as,  §,  J,  -£$. 

87.  An  Improper  Fraction  is  one  whose  numerator  equals  or 
exceeds  its  denominator;  as,  -f,  f,  V°. 

88.  A  Mixed  Number  is  one  expressed  by  an  integer  and  a 
fraction;  as,  3J,  read  three  and  one- fourth;  the  word  and  being 
placed  between  the  integer  and  fraction. 

89.  A  Complex  Fraction  is  one  which  has  a  fraction  in  one 

or   both  of  its    terms;    as,  y  — T  T^"'    The  first  is  read  one-half 
over  two-thirds,  etc. 

90.  A  Compound  Fraction  consists  of  two  or  more  single 
fractions  joined  together  by  the  word  of;  as,  ^  of  f  of  f . 

91.  Reduction  is  changing  the  form  of  a  number  or  fraction 
without  changing  its  value;  2  may  be  changed  to  f ;  3  to  *£-\  $  to 
3;  f  to  i,  while  the  value  is  not  altered. 

A  Fraction  is  an  indicated  division,  the  numerator  being  the 
dividend,  the  denominator  being  the  divisor  and  the  value  of  the 
fraction  the  quotient. 

The  value  of  the  fraction  is  the  ratio  existing  between  the 
numerator  and  denominator.  Therefore, 

1.  Increasing  the  numerator  increases  the  value  of  the  fraction. 

2.  Diminishing  the  denominator  increases  the  value  of  the 
fraction. 

3-  Diminishing  the  numerator  diminishes  the  value  of  the  frac- 
tion. 

4.  Increasing  the  denominator  diminishes  the  value  of  the 
fraction. 


46  NEW   BUSINESS   ARITHMETIC 

5.  Increasing  both  numerator  and  denominator  the  same  num- 
ber of  times  does  not  alter  the  value  of  the  fraction,  for  the  ratio 
between  them  remains  the  same. 

6.  Diminishing  both  numerator  and  denominator  in  the  same 
proportion  does  not  alter  the  value  of  the  fraction. 

REDUCTION  OF  FRACTIONS 

92.  Reduction  of  Fractions  consists  in  changing  their  form 
without  altering  their  value. 

A  fraction  is  in  its  lowest  terms  when  its  numerator  and  de- 
nominator have  no  common  divisor. 

As  fractions  may  be  reduced  to  lower  terms  by  division,  they 
may  also  be  reduced  to  higher  terms  by  multiplication. 

ORAL     PROBLEMS 

1.  -J  =  how  many  whole  ones?     f,  f,  -J-,  f. 

2.  -f  =  how  many  fourths?     How  many  halves? 

0  6         _    f       1       t        I          1          » 

#•  TT  —  tf,  7,   ?,    2T>  T5,  TS- 

1  l  «  _        *       III 
4-  32"  —  T^>  ¥>  ¥>  ?• 

5.  Change  f  f  to  thirds. 

6.  Change  f  1  to  twelfths,  to  sixths,  to  thirds. 

7.  How  many  halves  in  \\,  •&,  if,  II? 
5.  How  many  thirds  in  |,  -J-J,  f  f,  f  |? 

9.     Compare  |  with  if;  I  with  }-jj-;  $  with  ff. 

93.  To  reduce  fractions  to  their  lowest  terms. 
1.  Reduce  |%  to  its  lowest  terms. 

SOLUTION 
»)«=« 


3)11  =  I 

From  the  solution  we  have  the  following  rule: 

To  Reduce  Fractions  to  Lowest  Terms 

a.  Divide  both  terms  of  the  fraction  by  any  number  that  will 
divide  them  without  a  remainder. 

b.  Divide  this  result  as  before,  and  so  continue  to  divide  until 
no  number  will  divide  both  without  a  remainder. 


FRACTIONS  4  7 

c.  The  last  result  will  be  the  fraction  in  its  lowest  terms. 


2.  Reduce  iff  to  its  lowest  terms,  HI,  ftf, 

3.  Reduce  the  following  to  their  lowest  terms :  |fj,  ff $, 

rVA,  rfftV,  &&• 

4.  Express  in  its  simplest  form  the  quotient  of  125  divided  b} 
625. 

5.  Express  in  its  simplest  form  the  quotient  of  272  divided  by 

425. 

6.  Divide  873  by  3395  and  express  the  quotient  in  the  lowest 
terms  or  simplest  form. 

7.  Divide  323  by  437  and  express  the  quotient  in  the  lowest 
terms  or  simplest  form. 

ORAL     PROBLEMS 

1.  In  one  apple  are  how  many  halves?  4ths? 

2.  Two    peaches    equal    how    many    half    peaches?    fourth 
peaches  ? 

8.  -|  equals  how  many  4ths  ?  8ths  ?  12ths  ? 

4.  i  equals  how  many  8ths?  12ths?  24ths?  36ths? 

5.  |  equals  how  many  8ths?  12ths?  24ths?  36ths? 

6.  f  equal  how  many  8ths?  12ths?  24ths?  36ths? 

7.  f  equals  how  many  8ths?  12ths?  24ths?  36ths? 

8.  f  equal  how  many  IGths?  24ths?  40ths?  64ths? 

9.  |  equal  how  many  16ths?  24ths?  40ths?  64ths? 

10.  How  many  36ths  in  |  ?  in  f  ?  in  T%  ? 

11.  How  many  48ths  in  f  ?  f  ?  TV  A?  A? 

94.   To  reduce  fractions  to  higher  terms. 
Since  fractions  are  reduced  to  lower  terms  by  dividing  both 
terms  by  a  common  factor,  they  are  reduced  to  higher  terms  by 
multiplying  both  terms  by  a  common  factor. 

1.  Reduce  f  to  a  fraction  having  20  for  its  denominator. 

SOLUTION 
20  -T-  4  =  5 
j}_  X  5  =  15 
4    X   5  =  20 
Therefore  we  have  the  following  rule: 


48  NEW  BUSINESS  ARITHMETIC 

To  Reduce  Fractions  to  Higher  Terms 

a.  Divide  the  required  denominator  by  the  denominator  of  the 
fraction  in  order  to  find  how  many  times  the  terms  of  the  fraction 
must  be  increased. 

b.  Multiply  both   terms   of  the  fraction   by    the   quotient    as 
found  above. 

2.  Reduce  f  to  a  fraction  whose  denominator  is  15. 

3.  Reduce  f  to  a  fraction  whose  denominator  is  35. 

4.  Reduce  f  to  a  fraction  whose  denominator  is  63. 

5.  Reduce  TV  to  a  fraction  whose  denominator  is  180. 

6.  Reduce  ^f  to  a  fraction  whose  denominator  is  128. 

7.  Reduce  if  to  a  fraction  whose  denominator  is  375. 

8.  Reduce  j7^  to  a  fraction  whose  denominator  is  896. 

9.  Reduce  |f§  to  a  fraction  whose  denominator  is  918. 
10.  Reduce  -f  Jf  to  a  fraction  whose  denominator  is  2840. 

95.  To  reduce  improper  fractions  to  whole  or  mixed  numbers. 

ORAL     PROBLEMS 

1.  What  is  a  unit?     What  is  a  mixed  number? 

2.  How  many  ones  in  -f?  -f?  |?  \2? 

3.  How  many  ones  in  y?  V?  ¥?  if? 

4.  Reduce  to  units  V,  ¥,  V,  W- 

5.  VT  ===  7i;  7i  is  a  mixed  number. 

6.  *£•  =  how  many  units  and  what  part  of  a  unit? 

7.  -V  =  what  mixed  number?  ¥?  V?  V? 

8.  Reduce  to  whole  or  mixed  numbers:  -2g5,  ¥>  "V",  f  <L  V,  V» 

-v,  y. 

WRITTEN    PROBLEMS 

1.  Reduce  &f-  to  a  whole  or  mixed  number. 

SOLUTION 

-6_6-  =  66V  8  =  8|  =  8J 
Therefore : 

To  Reduce  Improper  Fractions  to  Integer  or  Mixed  Numbers 
a.  Divide  the  numerator  by  the  denominator. 
NOTE. — 1.  When  the  denominator  is  an  exact  divisor  of  the  numerator, 
the  result  will  be  a  whole  number. 


FRACTIONS  49 

2.  In  all  answers  containing  fractions  reduce  the  fractions  to  their 
lowest  terms. 

2.  Reduce  \6-  to  a  whole  or  mixed  number. 

3.  Reduce  &f-  to  a  whole  or  mixed  number. 

4.  In  ^p  of  a  bushel,  how  many  bushels  ? 

5.  In  J-f"8-  of  a  mile,  how  many  miles  ? 

6.  In  5^  of  a  pound,  how  many  pounds  ? 

7.  In  V46  of  a  vard,  now  many  yards  ? 

5.  In  -6T255  of  a  gallon,  how  many  gallons  ? 
9.  In  \462-  of  a  day,  how  many  days  ? 

10.  In  W3-of  an  apple,  how  many  apples? 

11.  Reduce  4T\6  of  a  foot  to  feet. 

.7,2.  Reduce  ^J-8  of  an  hour  to  hours. 
IS.  Reduce  ^H-0-  of  an  ounce  to  ounces. 

14.  Reduce  if  j^-  to  an  integer. 

15.  Reduce  m&  to  an  integer. 

16.  Reduce  J-Jp  to  an  integer. 

96.  To  reduce  whole  or  mired  numbers  to  fractional  form. 

ORAL     PROBLEMS 

1.  How  many  halves  in  2?  in  4?  in  16?  in 

2.  How  many  halves  in  2  J  ?  in  7|  ?  in  9  J  ? 

3.  How  many  thirds  in  8^?  in  15?  in  15  J? 

4.  12}  =  i;  16t  = 


WRITTEN    PROBLEMS 

Ja.  Reduce  24  yards  to  fourths. 

SOLUTION 

24 


4 
Ib.  Reduce  8|  to  an  improper  fraction. 

SOLUTION 

8§ 
3_ 

26 
3 


50  NEW   BUSINESS  ARITHMETIC 

Therefore,  we  have  the  following  rule: 
To  Reduce  Whole  and  Mixed  Numbers  to  Improper  Fractions 

a.  Multiply   the  whole   number   by   the  given   denominator 
and  write  the  product  over  the  given  denominator.  Or 

b.  Multiply   the  whole  number  by  the   denominator  of  the 
fraction,  to  the  product  add  the  numerator  and  write  the  result 
over  the  denominator. 

NOTE. — A  whole  number  is  reduced  to  a  fractional  form  by  writing  1 
under  it  for  a  denominator ;  thus,  9  =  f- . 

2.  In  15  dollars,  how  many  thirds  of  a  dollar? 

3.  In  46  bushels,  how  many  fifths  of  a  bushel? 

4.  In  89  gallons,  how  many  sixths  of  a  gallon? 

5.  How  many  fifteenths  in  28  feet? 

6.  How  many  twenty-fifths  in  36  tons? 

7.  How  many  thirtieths  in  45? 

8.  Reduce  92  to  fortieths. 

9.  Reduce  108  to  sixty-fourths. 

10.  Reduce  215  to  seventy-sixths. 

11.  Change  36  to  the  form  of  a  fraction. 

12.  Change  175  to  the  form  of  a  fraction. 

13.  Change  320  to  a  fraction  whose  denominator  shall  be  8. 

14.  Change  536  to  a  fraction  having  24  for  its  denominator. 

15.  Express   49   as  a   fraction   with  the   same   denominator 
as«. 

16.  In  5J  dollars,  how  many  half  dollars? 

17.  In  23 J  weeks,  how  many  fourths  of  a  week? 

18.  In  123|  pounds,  how  many  sixths  of  a  pound? 

19.  Express  27^  as  an  improper  fraction. 

20.  Express  66£  as  an  improper  fraction. 

21.  Express  15^  as  an  improper  fraction. 

22.  Reduce  23 -y  to  an  improper  fraction. 

23.  Reduce   234 ^J  to  an   improper   fraction. 
24-  Reduce  1078 T\  to  an  improper  fraction. 

25.  Reduce   1186  \\  to  an  improper   fraction. 

26.  Reduce  2300  Jf  to  an  improper  fraction. 

97.  To  reduce  two  or  more  fractions  to  the  least  common 
denominator. 


FRACTIONS  51 

A  Common  Denominator  is  a  denominator  common  to  sev- 
eral fractions.  Thus,  in  the  fractions  f,  f  and  f  the  common 
denominator  is  7. 

The  Least  Common  Denominator  of  several  fractions  is  the 
least  denominator  to  which  all  can  be  reduced.  It  is  the  least 
common  multiple  of  their  denominators. 

ORAL     PROBLEMS 

1.  -J  =  how  many  4ths?  8ths?  24ths? 

2.  f  =  how  many  12ths?  24ths?  36ths? 

3.  f  =  how  many  12ths?  24ths?  36ths? 

4.  |  and  f  each  =  how  many  12ths?  24ths? 

5.  Change  f  and,  f  each  to  48ths,  24ths. 

6.  Change   §•  and  f  each  to  a  fraction  having  the  same 
name. 

7.  Change  f-  and   f  each  to  63ds.     63  is  the  L.  C  D.  of 
these  fractions. 

8.  Reduce  f  and  f  to  their  L.  C.  D. 

9.  Reduce  J,  f  and  f  to  their  L.  C.  D. 

10.  Reduce  |,  i,  1  and  A  to  their  L.  C.  D.  (24ths). 

WRITTEN    PROBLEMS 

1.  Reduce  I,  I  and  -f  to  their  least  common  denominator. 

SOLUTION 

2)4,6,8  2X^X3X2  =  24 

2)2,3,4  }  =  H 


We  therefore  have  the  following  rule  : 
To  Reduce  Fractions  to  Their  Least  Common  Denominator 

a.  Find  the  least  common  multiple  of  the  given  denominators 
and  write  this  as  the  new  denominators  of  the  fractions. 

b.  Divide  this  common  denominator  by  each  of  the  given  de- 
nominators and  multiply  each  numerator  by  the  corresponding 
quotient.    The  product  will  be  the  new  numerator. 


NEW  BUSINESS  ARITHMETIC 

NOTE. — Reduce  mixed  numbers  to  improper  fractions  and  all  fractions 
to  the  lowest  terms  before  beginning  the  operation. 

2.  Reduce  i,  £  and  -J  to  their  least  common  denominator. 
8.  Reduce  f ,  f  and  ^  to  their  least  common  denominator. 

4.  Reduce  %,  A»  TST  and  H  to  their  least  common  denomi- 
nator. 

5.  Reduce  f ,  |i,  \\  and  iJ  to  their  least  common  denomi- 
nator. 

6.  Reduce  £,  \,  £,  J  and  -£%  to  their  least  common  denomi- 
nator. 

7.  Reduce  f,  i,  T3o,  A  and  £J  to  their  least  common  denomi- 
nator. 

5.  Reduce  f,  f ,  f,  A  and  -}-t  to  their  least  common  denomi- 
nator. 

P.  Reduce  £,  f ,  },  A»  A  and  A  to  their  least  common  de- 
nominator. 

10.  Change  f,   A,   3f,  9  and  1  to  fractions  having  the  least 
common  denominator. 

11.  Change  f  J,  If,  £,  H  and  6  to  fractions  having  the  least 
common  denominator. 

12.  Change  f ,  ^f  A,  A,  it  and  |}  to  fractions  having  the 
least  common  denominator. 

IS.  Change  &,  f ,  f  and  A  to  fractions  having  the  least  com- 
mon denominator. 

14..  Change  J,  f ,  f,  f,  li,  ||  and  |J  to  fractions  having  the 
least  common  denominator. 

15.  Change  s\,  6£,  A>  ?,  f  and  1J  to  fractions  having  the 
least  common  denominator. 

ADDITION  OF  FRACTIONS 

98.  Addition  of  Fractions  is  the  process  of  finding  the  sum 
of  two  or  more  fractional  numbers. 

We  have  seen  that  no  quantities  can  be  added  together  except 
they  are  of  the  same  kind  or  denomination.  Not  only  must  frac- 
tions be  parts  of  the  same  kind  of  units,  but  they  must  have  the 
same  denominators  before  they  can  be  added. 


FRACTIONS  53 

ORAL     PROBLEMS 

1.  What  is  the  sum  of  J,  f  and  |? 

2.  What  is  the  sum  of  f,  f\  and  J? 

5.  A  has  J  and  B  f.     How  many  eighths  have  both?     How 
many  units? 

4.  Find  the  sum  of  ^  and  ^  ;  J  and  J  ;  J  and  J. 

5.  Find  the  sum  of  §  and  |  ;  f  and  f  ;  f  and  f  . 
0.  Find  the  sum  of  f  and  f  ;  J  and  f  ;  T72  and,  f  . 

7.  Find  the  sum  of  2J  and  3£  ;  4  J  and  5  J  ;  3£  and  4J. 
5.  Find  the  sum  of  3|  and   6j;    3f  and  4&;  7f  and  J. 
0.  One  boy  has  $3|  and  another  has  $2J.     How  many  dol- 
lars have  both? 

10.  A  boy  rode  3J  miles  in  a  wagon,  11  J  miles  in  a  train,  and 
walked  2^  miles.     How  far  did  he  go  in  all? 

11.  How  many  years  are  12f  years  and  18J  years? 

12.  How  many  hours  are  15f  hours  and  17J  hours? 

13.  What  is  the  sum  of  3J  bushels,  4J  bushels  and  5f  bushels? 

14.  How  many  dollars  in  $2J  +  $3|  +  $6T7^  and 

WRITTEN  PROBLEMS 

1.  Find  the  sum  of  J,  f,  f  and  f  . 

SOLUTION 

The  L.  C.  M.  of  2,  3,  4  and  6  is  12. 
4  =  A 


A  +  A  +  A  +  «=«  =  «A  =  af  . 

From  the  preceding  problem  and  explanation  we  have  the  fol- 
lowing : 

To  Add  Fractions 

a.  Reduce  the  fractions  to  their  least  common  denominator. 

b.  Add  the  numerators  and  under  their  sum  write  the  denomi- 
nator. 

c.  In  mixed  numbers,  add  the  whole  numbers  and  fractions 
separately,  then  add  their  sums. 


64  NEW  BUSINESS   ARITHMETIC 

NOTE. — If  the  mixed  numbers  are  small,  they  may  be  reduced  to  im- 
proper fractions,  and  then  added  after  the  usual  method. 

2.  Add  i,  f ,  f  and  f.  6.  Add  {,  £,  1  and  H- 

3.  Add  A,  A,  A  and  A-  7.  Add  *,  A,  H  and  If. 

4.  Add  I,  |,  i  and  A  8.  Add  7f,  9f,  llf  and  9f. 

5.  Add  |,  i,  i  and  i  P.  Add  6f,  7TV,  8}i  and  9^. 

10.  What  fraction  is  equal  to  1£  +  2f  +  3}  +  4f  +  5f  + 
6f? 

11.  What  is  the  sum  of  17f,  18T5¥,  26^  and  lOf  ? 
1£.  Add  41,  ITS,  2ff,  Sf*  and  5 A. 

13.  What  fraction  is  equal  to£  +  i  +  i  +  A  +  A  +  A? 

14.  What  is  the  sum  of  125f,  327A  and  25i? 

15.  What  is  the  sum  of  iff,  8f,  3 A  and  14|? 

15.  I  have  four  fields.  The  first  contains  17J  acres;  the  sec- 
ond, llf-  acres;  the  third,  21f  acres;  the  fourth,  19 A  acres. 
How  many  acres  have  I  ? 

17.  Jones  paid  $7|  for  a  coat,  $2J  for  a  hat,  $3|-  for  pants, 
$1£  for  a  vest  and  $4f  for  shoes.     What  did  he  pay  for  all  ? 

18.  A  merchant  bought  38J  yard,s  of  calico,  103f  yards  of 
muslin,  80f  yards  of  flannel  and  26J  yards  of  gingham.     How 
many  yards  did  he  buy? 

19.  A  family  used  f  of  a  ton  of  coal  in  September,  T7^  of  a  ton 
in  October,  |    of  a  ton  in  November,  ff  of  a  ton  in  December 
and  1J  tons  in  January.     How  much  did  they  use  in  the  five 
months  ? 

20.  A  farmer  received  $7£  for  a  hog,  $23 J  for  a  cow,  $11| 
for  a  sheep  and  $123  A  f°r  a  horse.     How  much  did  he  receive 
for  all? 

21.  A  man  invested  $2460f  in  land,  $1432. f     in  cotton  and 
$1314f  in  mining  stock.     What  was  his  total  investment? 

22.  A  has  on  deposit  in  a  savings  bank  $46f ,  B  has  on  deposit 
$28A,  C  has  on  deposit  $76J  and  D  has  on  deposit  $96|.     What 
is  the  total  amount  of  their  deposits? 

28.  A  collector  received  from  one  man  $5^%,  from  another 
$11|,  from  another  $18T%,  and  from  another  $lf.  How  much 
did  he  collect  in  all? 


FRACTIONS  55 

£4.  Add  1026H,  1875|,  5634f  and  4327f. 

25.  A  lady  went  shopping,  and  expended  for  car  fare  J  of  a 
dollar,  for  thread  £J  of  a  dollar,  for  needles  TV  of  a  dollar,  for 
gloves  1J  dollars,  for  a  hat  7J  dollars,  for  a  dress  32  ^  dollars. 
What  was  the  total  amount  of  her  expenditures  ? 

26.  A  farmer  sold  437£  bushels  of  corn   for    $127i;  268T52 
bushels  of  wheat  for  $186T7<y ;  728f-  bushels  of  oats  for  $245tt 
and  421f  bushels  of  rye  for  $216?V     How  many  bushels  d,id  he 
sell  and  what  was  the  total  sum  received? 

27.  A  merchant  bought  four  pieces  of  gingham  containing 
the  following  number  of  yards  in  each  piece:  43i,  44 J,    45  and  46| 
(generally  written  431,  442,  45  and  463).     How  many  yards  did 
he  buy? 

28.  How  many  yards  in  the  following  pieces  of  denim:  361, 
421,    41,    39,    382,    43,    443,    462,    41,    381,    392,    34,    363,    38, 
412,  42,  411,  431,  442,  45,  46,  44,  433  and  462  ? 

SUBTRACTION  OF  FRACTIONS 

99.  Subtraction  of  Fractions  consists  in  finding  the  differ- 
ence between  two  fractional  numbers. 

Since  quantities  of  different  kinds  or  denominations  cannot  be 
subtracted  it  follows  that  in  order  to  subtract  fractions  they  must 
be  parts  of  the  same  kind  of  units  and  must  have  the  same  de- 
nominators. 

ORAL     PROBLEMS 

1.  Find  the  value  of  $2  less  $| ;  $4  less  $£. 

2.  Find  the  value  of  $3£  less  $1 J ;  $5}  less  $2J. 

3.  Find  the  difference  between  J  and  f ;  f  and  f . 

4.  If  you  spend  J  and  £  of  your  money,  what  part  remains  ? 

5.  From  J  of  a  barrel  of  sugar  f  was  sold.     What  part 
remains  ? 

6.  7|  inches  and  how  many  inches  make  one  foot? 

7.  15|  hours  and  how  many  hours  equal  one  d,ay? 

8.  7f  feet  from  3  yards  leave  how  many  feet? 

9.  3J  +  2^  +  3J  +  2|  from  15ft  =  ? 
10.  7J  +  8J  from  lOf  +  6J  =  ? 


56  NEW   BUSINESS   ARITHMETIC 

WRITTEN  PROBLEMS 

1.  From  §  subtract  f. 

SOLUTION 

TheL.  C.  M.  of  3  and  8  is  24. 

*  =  =  tt  H  -  -  A  =  A 

I  =  ih 

From  this  we  derive  the  following  rule : 

To  Subtract  Fractions 

a.  Reduce  the  fractions  to  their  least  common  denominator. 

b.  Subtract  the  numerators  and  under  the  difference  write  the 
denominator. 

c.  Reduce  the  result  to  its  lowest  terms. 

NOTE. — To  subtract  mixed  numbers,  if  they  are  small,  reduce  them  to 
improper  fractions  and  subtract  the  less  from  the  greater ;  if  they  are 
large,  reduce  the  fractions  to  a  common  denominator  and  then  subtract 
the  subtrahend  of  both  integers  and  fractions  from  the  minuend  of  both 
integers  and  fractions. 

2.  From  |  take  J.  8.  From  251  take  11TV 

3.  From  H-  take  T4T.  9.  From  8£  take  3j. 

4.  From  •&•  take  i  10.  From  4|  take  if 

5.  From  if  take  &.  11.  Subtract  2j  from  13. 

6.  From  |f  take  TV  12.  Subtract  130f  from  285J. 

7.  From  11|  take  7}.  13.  Subtract  ||  from  4jf . 
U.  Subtract  fW  from  fff. 

15.  Find  the  difference  between  ||  and  ^. 

itf.  Find  the  difference  between   20|  and  9J|. 

17.  Find  the  difference  between  5||  and  3|. 

15.  A  boy  who  had  $5  lost  $lf.    How  much  had  he  left? 

19.  I  paid  $23f  for  a  cow  and  $19  for  some  sheep.    How  much 
more  did  the  cow  cost  than  the  sheep  ? 

20.  A  clerk  received  $14J  for  a  week's  work  and  spent 
of  it.    How  much  did  he  have  remaining? 

.21.  A  teacher  who  receives  $75  for  a  month's  work,  paid 
for  board,  $1J  for  light  and  $9|  for  clothes.    How  much  of  it  did 
he  have  at  the  end  of  the  month  ? 


FRACTIONS  57 

22.  A  man  having  $S7f,  paid  $23f  for  a  coat,  $12T%  for  a  pair 
of  pants,  $4 1 -J  for  a  vest,  $5  for  a  hat  and  $TV  for  a  neck-tie.  How 
much  money  had  he  left  ? 

5-3.  A  father  having  $7500,  divided  it  among  his  four  children 
as  follows  :  To  the  eldest  he  gave  $2375f ;  to  the  second  he  gave 
$1843  A;  to  the  third  $2162f ;  and  to  the  fourth  the  remainder. 
How  many  dollars  did  the  fourth  receive  ? 

24.  A  merchant  bought  flour  at  $7§  per  barrel  and  sold  it  at 
$8J.    What  did  he  gain  per  barrel  ? 

25.  From  the  sum  of  25  rV  and  9  take  the  sum  of  3J  and  llf . 

26.  A  grocer  having  $1000  in  money,  expends  $324f  for  flour, 
$128J  for  sugar,  $48f  for  canned  goods,  $76i  for  coffee,  $98i| 
for  tea,  $216f    for  sundry  other  articles,  and  pays  one  month's 
rent  of  his  store,  $50.     How  much  money  has  he  remaining? 

27.  From  the  sum  of  56-&  and  89J  take  the  difference  between 
5f  and  81TV 

2S.  A  farmer  had  three  fields.  The  first  contained  320H 
acres,  the  second  225f  acres  and  the  third,  IGOf  acres.  He  sold 
540f  acres.  How  many  acres  had  he  left? 

29.  A  bought  6|  pounds  of  A  sugar,  4{  pounds  of  B  sugar, 
7|  pounds  of  C  sugar  and  11J  pounds  of  granulated  sugar.     He 
found  5J|  pounds  to  be  damaged.     What  was  the  weight  of  the 
good  sugar  received? 

30.  A  real  estate  dealer  bought  a  house  and  lot  for  $3100. 
He  paid  $218£  for  repairs;  $290T8=>  for  taxes;  $16&  for  advertis- 
ing and  $38f  for  expenses  in  selling  it.    He  collected  $37£  in  rent 
for  the  property  while  he  owned  it,  and  sold  it  for  $4000  in  cash. 
How  much  was  his  gain? 

MENTAL  REVIEW  OF  ADDITION  AND  SUBTRACTION 

10O.  To  add  two  fractions  whose  numerators  are  each  1, 
take  the  sum  of  the  denominators  for  the  numerator,  and  the  prod- 
uct of  the  denominators  for  the  denominator  of  the  sum. 
Thus,  }  +  1  =  A. 


58  NEW   BUSINESS   ARITHMETIC 

Find  the  value  of: 

i.  i+f     e.  i+f     a. 

2.  i+f         7.  TV+i  m  i+f 

3.  i+f         5.  i+A.  13.  i+rV. 
-4.  i+f        5.  i+f  14.  m. 
5.  i+A-.  m  i+f  J5.  i+f 

100  A.  To  subtract  fractions  whose  numerators  are  each  1, 
take  the  difference  of  the  denominators  for  the  numerator  and  the 
product  of  the  denominators  for  the  denominator  of  the  remainder. 
Thus,  i—  i=Vo. 

Find  the  value  of  : 


5.  i-i  9. 

6.  i-i  10.  J-4. 
5.  i-i                     7.  *—  A.  iJ.  f-  1. 

4.  1-i.  «.  i-i.  w.  i-i. 

100B.  To  add  two  fractions  whose  numerators  are  greater 
than  1,  take  the  sum  of  the  products  of  the  numerator  of  each  by 
the  denominator  of  the  other  for  the  numerator,  and  the  product 
of  the  denominators  for  the  denominator  of  the  sum.  Thus,  f  -f- 
}=}}.  (2  X  4  +  3  X  3  =  17,  and  3  X  4  =  12.) 

Find  the  value  of: 


1.  f+t.  5.  t+i  9. 

e.  m.          10.  m. 

7.    |+f  W.    f+T3T. 

4.  *+f  «.  i+f  ^.  4+i 

100C...  To  subtract  two  fractions  whose  numerators  are 
greater  than  1,  take  the  difference  of  the  products  of  the  numera- 
tor of  each  by  the  denominator  of  the  other  for  the  numerator,  and 
the  product  of  the  denominators  for  the  denominator  of  the  re- 
mainder. Thus,  f  —  f  =  TV  (3  X  3  —  2  X  4  =  1,  and  3  X  4 
=  12.) 

MULTIPLICATION  OF  FRACTIONS 

101.  A  fraction  is  multiplied  by  multiplying  the  numerator 
or  dividing  the  denominator. 


FRACTIONS  59 

ORAL     PROBLEMS 

1.  At  $i  for  1  dozen  eggs,  what  is  the  cost  of  3  dozen? 

2.  At  $|  for  a  chicken,  what  will  5  chickens  cost? 

3.  If  a  boy  has  f  of  a  bushel,  what  would  5  boys  have  ? 

4.  3  times  J  =  t;  6  X  i  ==  t;  8  X  1  ==  i;  9  X  \  ==  J-. 

5.  5  times  J  =  i;  5  X  f  =  .r;   5  X  1  =  x;    5  X  |  =  *. 

6.  7  times  f  =  T;  7  X  f  —  ,r;  7  X  f  =  .r;  7  X  |  =  x. 

7.  4  times  lj  —  x\  4  X  2J  =  x\  4  X  3|  =  x\    4  X  2f  =  x. 
S.  If  a  man  earns  $2J  a  day,  how  much  will  he  earn  in  4 

days? 

9.  If  a  bushel  of  clover  seed  costs  $2f,  what  will  5  bushels 
cost? 

10.  6  X  31  =  x\  7  X  2f  =  ;r;  8  X  if  =  x\  9  X  J  =  x. 

102.  To  multiply  a  fraction  by  a  whole  number. 

WRITTEN  PROBLEMS 

1.  If  1  hat  costs  |  of  a  dollar,  what  will  6  hats  cost? 

SOLUTION  EXPLANATION.—  Since  1  hat  cost  3- 

fourths  of  a  dollar,  6  hats  will  cost  6 

"  —  =  4f  =  4£  times  3-fourths  of  a  dollar  or  18- 
fourths  of  a  dollar,  which  is  $4^. 

NOTE.  —  Always   divide  the  denominator  when  it  is   exactly  divisible 
by  the  multiplier. 

2.  Multiply  f  by  5.  7.  Multiply  TV  by  12. 

S.  Multiply  A  by  9.  8.  Multiply  if  by  9. 

4.  Multiply  f  by  4.  9.  Multiply  T\V  by  27. 

5.  Multiply  rV  by  6.  10.  Multiply  |f  by  14. 

6.  Multiply  A  by  10.  H.  Multiply  T<yV  by  8. 

J#.  If  a  man  earn  9f  dollars  per  week,  how  many  dollars  can 
he  earn  in  7  weeks  ? 

13.  Multiply  125f  by  6. 

SOLUTION 

125J 


750 
754^ 


60  NEW  BUSINESS   ARITHMETIC 

14.  Multiply  315f  by  9.  15.  Multiply  256&  by  15. 

16.  Multiply  80T%  by  14. 

11.  Find  the  cost  of  12  yards  of  ribbon  at  $f  per  yard. 

18.  Find  the  cost  of  128  bushels  of  oats  at  $f  per  bushel. 

19.  At  $J  per  pound  what  will  16  pounds  of  butter  cost? 

20.  If  a  ton  of  hay  cost  $11}  what  will  15  tons  cost? 
103.  To  multiply  a  whole  number  by  a  fraction. 

.   ORAL     PROBLEMS 

1.  At  $4  per  bushel  what  will  \  of  a  bu.  cost? 

2.  At  $9  per  ton  what  will  -J  of  a  ton  cost? 

3.  What  is  |  of  8  ;  J  of  12 ;  i  of  13  ;  i  of  15  ? 

4.  What  is  i  of  12;  i  of  16  ;  i  of  24;  i  of  36? 

5.  What  is  }  of  12 ;  f  of  16  ;  }  of  24 ;  f  of  36  ? 

6.  What  is  J  of  17 ;  $  of  25 ;  -J  of  35 ;  £  of  51  ? 

7.  What  is  f  of  17  ;  f  of  25  ;  f  of  35 ;  f  of  51? 

8.  |  X  15  =  x\  f  X  21  =  x\  18  X  |  =  x\  15  X  f-  =  #. 

WRITTEN  PROBLEMS 

1.  At  $9  per  ton  what  will  f  of  a  ton  of  coal  cost  ? 

SOLUTION 

9 

_2 

3)18 

6 

From  this  solution  we  see  that  multiplying  by  a  fraction  con- 
sists in  multiplying  by  the  numerator^  and  dividing  by  the  denomi- 
nator. 

2.  Multiply  5  by  T\.  5.  Multiply  120  by    if. 

3.  Multiply  32  by  f .  6.  Multiply  105  by  Jf. 

4.  Multiply  100  by  &.  7.  Multiply  86  by  f  f . 

8.  At  $9  a  bushel  what  will  f  of  a  bushel  of  clover  seed  cost  ? 

9.  Multiply  184  by  6f. 

SOLUTION 

184  EXPLANATION.— Multiply  by  the  fraction  ^ 

6f  and  the  whole  number  (?,  and  add  the  products 

115  =  |  X  184  together.  The  result  will  be  the  product  re- 

1104  quired. 

1219 


FRACTIONS  61 

10.  Multiply  52  by  8J.  12.  Multiply  135  by26f. 

11.  Multiply  76  by  11-J.  13.  Multiply  258  by   42  H- 

14.  Multiply  156  by  f  J. 

15.  If  a  railroad  train  runs  36  miles  an  hour,  how  far  will  it 
run  in  15jf  hours? 

16.  If  a  mill  is  worth  $2650  and  B  owns  T%  of  it,  how  much 
is  B's  share  worth? 

17.  What  will  216  barrels  of  pork  cost  at  $6f  per  barrel? 
IS.  At  $2J  a  cord,  what  will  18  cords  of  wood  cost? 
104.  To  multiply  a  fraction  by  a  fraction. 

ORAL     PROBLEMS 


1.  If  i  of  |  is  i  what  is  J  of  |? 

2.  If  i  of  H  is  A-  what  is  |  of  If? 
8.  What  is  |  of  i?  }  of  A?  |  of  if. 

4.  What  is  i  of  f?  i  of  f  ?  i  of  }? 

5.  What  is  f  of  i?  f  of  f  ?    f  of  }? 


WRITTEN  PROBLEMS 

1.  What  will  i  of  a  yard  of  flannel  cost  at  f  of  a  dollar  per 
yard? 

SOLUTION 

2 

nr     #     v  _T_  - 

or,  -T-  X  -v-  — 


3 

Therefore  we  have  the  following  rule : 

To  Multiply  Fractions 

a.  Reduce  mixed  numbers  to  improper  fractions. 

b.  Multiply  the  numerators  together  and  multiply  the  denom- 
inators together.     Under  the  product  of  the  numerators,  write 
the  product  of  the  denominators. 

c.  Reduce  to  its  simplest  form. 

NOTE. — Cancel  all  factors  common  to  numerators  and  denominators." 

2.  Multiply  J  by  |.  5.  Multiply  4i  by  f . 

3.  Multiply  I  by  |.  6.  Multiply  2|  by  19|. 

4.  Multiply  H  by  f|.  7.  Multiply  16|  by  40rV 


62  NEW   BUSINESS   ARITHMETIC 

8.  Multiply  34f  by  ii        9.  Multiply  18T\  by  10  A. 

10.  What  is  the  product  of  f,  H  and  |? 

11.  What  is  the  product  of  2f,  f,  3  and  8§? 

12.  What  is  the  product  of  TV,  i  if  and  3J? 

13.  What  is  the  product  of  4J,  5J,  6|  and  7J  ? 

NOTE.  —  Fractions  with  the  word  of  between  them  are  sometimes  called 
compound  fractions.  The  word  of  is  simply  an  equivalent  for  the  sign  of 
multiplication,  X,  and  signifies  that  the  numbers  between  which  it  is  placed 
are  to  be  multiplied  together. 

14.  Multiply  f  of  /T  by  i  of  9J. 

15.  Multiply  f  of  5f  by  TV  of  38. 

16.  What  is  the  product  of  8,  §  of  7J,  J,  16  and  3J? 

17.  What  is  the  value  of  f  of  \  of  Jf  of  i? 
18..  What  is  the  value  of  £  of  f  of  f  of  H? 

IP.  What  fraction  is  equal  to  £  of  }  of  }  of  f  of  $  of  f  of  | 
off? 

#0.  A  man  owning  f  of  a  store  sold  §  of  his  share.  What  part 
of  the  whole  store  did  he  sell? 

21.  What  will  f  of  a  pound  of  tea  cost  at  f  of  a  dollar  per 
pound  ? 

Find  the  value  of  the  following-  expressions: 

22.  f  of  160.  27.  4J  X  9  X  i  of  18J. 

23.  84  X  f  .  28.  62^  times  f  of  T^  of  f  . 

24.  H  of  A.  #0-  i  of  25  X  T7o  of  26  J. 

25.  f  times  144.  30.   (i  +  T9o)  X  (t  +  4J). 
00.  T9TT  of  A  X  lj.                81.  (24  —  f)  X  (4|  —  3*). 
Where  the  mixed  numbers  are  large,  instead  of  reducing  them 

to  improper  fractions  they  may  be  multiplied  by  the  following 
method  : 

82.  Multiply  36|  by  9}. 

SOLUTION 


^  =  product  of  f  X  f  . 

27       =  product  of  36   X  f. 

3f     =  product  of  |X9. 

324      =  product  of  36  X   9- 
364A- 

Or,  36f  X  9f  =  *&  X        ==  3H9  or  354*. 


FRACTIONS  63 

S3.  Multiply  32f  by  7f .  34.  Multiply  86T9o  by  9f . 

35.  What  cost  128f  barrels  of  pork  at  $8f  per  barrel? 

36.  A  farmer  sold  17J  bushels  of  corn  at  $£  per  bushel.    How 
much  did  he  receive? 

37.  I  bought  23J  barrels  of  salt  at  $2^  each.     What  did  it 
cost  me? 

38.  A  farmer  sold  a  quarter   of   a   beef   that   weighed  523} 
pounds  at  5§c  per  pound.     How  much  did  he  receive  for  the 
quarter  ? 

39.  At  6§c  per  pound,  what  sum  would  be  received  for  3  hogs 
that  weighed  respectively  316f,  411T%  and  374^  pounds? 

40.  A  grain  dealer  bought  28f  bushels  of  rye  from  one  man 
and  47f  bushels  from  another.     He  paid  $lf  per  bushel.    What 
did  the  rye  cost  the  dealer  ? 

41.  In  1  rod  there  are  16  J  feet.     How  many  feet  are  there 
around  a  field  that  is  18f  rods  on  each  side  and  14T7e  rods  on 
each  end? 

42.  A  who  owned  J  of  a  mill  worth  $7200,  sold  f  of  his  share 
to  B.    How  much  did  B  pay  A,  and  what  part  of  the  mill  did  he 
buy? 

43.  L.  J.  Camp  sold  24  hogs  that  averaged  368^  pounds  at 
8fc  per  pound.    How  much  did  he  receive  for  the  hogs? 

44-  If  a  boy  earns  $1J  per  day,  how  much  would  he  earn  in 
f  of  4  weeks,  allowing  4  days  for  time  lost  by  sickness? 

45.  A.  K.  Case  bought  of  J.  M.  Sims  2J  dozen  eggs  at  lie 
per  dozen,  1J  pounds  of  Rio  coffee  at  32c  per  pound,  4  pounds  A 
sugar  at  9^c  per  pound,  3J  bushels  of  potatoes  at  30c  per  bushel, 
4  cans  of  tomatoes  at  12^c  per  can,  3  gallons  kerosene  at  life 
per  gallon,  ^  dozen  lemons  at  20c  per  dozen.     Find  the  total 
amount  of  the  purchase. 

46.  M.  N.  Oliver  bought  of  P.  S.  Rawson  3£  pounds  of  pork 
at  9c  per  pound,  5|  pounds  ham  at  12^c  per  pound,  8  pounds  beef 
at  8Jc  per  pound,  16  pounds  chicken  at  7fc  per  pound,  3  quarts 
oysters  at  13Jc  per  quart,  4J  pounds  bacon  at  lOJc  per  pound, 
2^  pounds  sausage  at  8c  per  pound,  12^  pounds  mutton  at  8Jc  per 
pound.    What  was  the  total  cost? 

47.  Mrs.  E.  M.  Cooper  bought  of  Cook  Bros.  4^  yards  of  rib- 


64  NEW   BUSINESS   ARITHMETIC 

bon  at  lOc  per  yard,,  3|  yards  of  muslin  at  6c  per  yard,  9J  yards 
drilling  at  Sc  per  yard,  7  yards  calico  at  5|c  per  yard,  11^  yards 
flannel  at  24c  per  yard,  9f  yards  carpet  at  30c  per  yard,  16  yards 
linen  at  10|c  per  yard,  12  J  yards  silk  at  $J  per  yard.  How 
much  should  Mrs.  Cooper  pay  Cook  Bros.? 

48.  I  bought  2  cords  of  wood  at  $5}  per  cord,  and  3^  tons  of 
coal  at  $7£  per  ton.     I  gave  the  merchant  two  20-dollar  gold 
pieces.  How  much  change  should  I  receive  ? 

49.  If  17 J  yards  of  broadcloth  are  bought  at    |-  of  7|  dollars 
per  yard  and  sold  at  J  of  $5r2i  per  yard,  what  is  the  gain  or  loss? 

DIVISION  OF  FRACTIONS 

105.  A  Fraction  is    divided  by    dividing   the    numerator  or 
multiplying  the  denominator.     (See  Sec.  92.) 

106.  To  divide  a  fraction  by  a  whole  number. 

ORAL  PROBLEMS 

1.  If  3  pounds  of  butter  cost  $f,  what  will  1  pound  cost? 

2.  If  6  pounds  of  cheese  cost   $}f  what  will  1  pound  cost? 

3.  Find  the  value  of  the  following :  f  -^-  3  =  x ;  j  f  -f-  6  =  x ; 
U  -*-  9  =  *;  ||  -  9  =  *;  \\  -*-  5  =  .r; 

4.  If  3  yards  of  calico  cost  $J,  what  will  1  yard  cost? 

5.  If  5  dozen  eggs  cost  $T75-,  what  will  1  dozen  cost? 

6.  Find  the  value  of  the  following :    j-^4  =  .r;J-^3=jir; 
f>f,7^4r;t-T-.9=Tjr. 

7.  A  paid  $6|  for  5  bushels  of  clover  seed,  what  did  he  pay 
per  bushel?    (6f  ==  V.) 

8.  I  paid  $5^  for  3  turkeys,  find  the  cost  of  each. 

9.  Find  the  value  of  the  following :    3J  -j-  5  =  x ;  16 J  -f-  10 
=  >;5t4-6==;r;8J  -r-  G  =  x. 

WRITTEN  PROBLEMS 

1.  If  3  bushels  of  timothy  cost  J  of  a  dollar,  what  will  1 
bushel  cost? 

SOLUTION 

L^~    3    =  JL 

¥  24 

NOTE. — We  divide  the  numerator  when  it  is  exactly  divisible  by  the 
•divisor;  otherwise  we  multiply  the  denominator. 


FRACTIONS  65 

2.  Divide  f  by  2.  6.  Divide  TVV  by  25. 

5.  Divide  T97  by  3.  7.  Divide  H  by  11. 

4.  Divide  ff  by  5.  8.  Divide  ff  by  21. 

5.  Divide  -f f  by  9.  P.  Divide  HI  by  75. 

.?#.  If  G  pounds  of  cheese  cost  J  of  a  dollar,  what  will   1 
pound  cost? 

11.  At  $4  a  yard  what  part  of  a  yard  of  broadcloth  can  be 
bought  for  /T  of  a  dollar? 

12.  If  7  dozen  eggs  cost  -J-|  of  a  dollar,  what  will  one  dozen 
cost? 

IS.  If  7  bushels  of  wheat  cost  $6} what  will  one  bushel  cost? 

NOTE. — Reduce  the  mixed  number  to  an  improper  fraction  and  divide 
as  before. 

14-  If  7  dozen  hammers  cost  $23^,  what  will  one  dozen  cost? 

15.  A  farmer  paid  $563f  for  4  horses.     How  much  did  he 
pay  for  each  ? 

16.  If  9  men  consume  j  of  5f  pounds  of  meat  in  a  day,  how 
much  does  each  man  consume  ? 

107.  To  divide  by  a  fraction. 

ORAL  PROBLEMS 

1.  If  coffee  can  be  bought  at  the  rate  of  $J  per  pound,  how 
many  pounds  can  be  bought  for  $i?  $|?  $J?  $J?  $f ?  $f ?  $£?  $|? 


2.  Find  the  value  of  the  following :    f-^i;|-^i;f-^-4; 

I  +•*;  f  •*••!? 

3.  Find  the  value  of  the  following :    f-i-f;f-7-f;$H-§; 

I  -*;*•**. 

4.  If  2^  bushels  of  oats  cost  $1-J  what  is  the  cost  of  one 
bushel? 

5.  Find  the  value  of  the  following:    3J-^  2J;  If  -^-  14;  3|  -f- 
1J;  5J  -f-  2J. 

108.  The  Reciprocal  of  a  number  is  1  divided  by  the  number ; 
thus  the  reciprocal  of  3  is  ^. 

109.  Since  the  reciprocal  of  a  number  is  1  divided  by  that 
number  the  reciprocal  of  a  fraction  is  that  fraction  inverted.     In- 
verting a  fraction  shows  how  many  times  it  is  contained  in  1. 

5 


66  NEW   BUSINESS   ARITHMETIC 

WRITTEN  ^PROBLEMS 

1.  At  f  of  a  dollar  a  yard,  how  many  yards  of  cloth  can  be 
bought  for  $9  ? 

SOLUTION 


From  the  foregoing  principles  and  explanation  we  derive  the 
following  rule  : 

To  Divide  Fractions 

a.  Reduce  whole  or  mixed  numbers  to  improper  fractions. 

b.  Invert  the  divisor,  and  multiply  the  dividend  by  the  divisor 
inverted. 

c.  Reduce  the  result  to  simplest  form. 

2.  Divide  1  by  f  .  5.  Divide  £  by  T\. 

3.  Divide  J  by  f  .  6.  Divide  f  by  ff 

4.  Divid,e  j  by  f  7.  Divide  J  by  H. 

5.  How  many  times  is  £  contained  in  f  ? 
P.  How  many  times  is  t%  contained  in  2J  ? 

.70.  How  many  times  is  -J-f  contained  in  3y9T? 

I-/.  How  many  times  is  J  of  f  contained  in  28? 

12.  How  many  times  is  f  of  f  of  J  contained  in  §  of  f  ? 

15.  How  many  times  is  f  of  -J  contained  in  f  of  H? 

14.  How  many  times  is  llf  contained  in  £  of  45^? 

75.  What  is  the  quotient  of  18  J  divided  by    3|? 

76.  What  is  the  quotient  of  f  of  8{  divided  by  7J? 

17.  What  is  the  quotient  of  ^  of  J  divided  by  4J  times  f  ? 
75.  What  is  the  quotient  of  f  of  J  of  f   divided  by  f  of  f 
ofi9o? 

19.  What  is  the  value  of    ~^? 

5i 

SOLUTION 


>.  What  is  the  value   of  HrJ 


FRACTIONS  67" 

8 

21.  What  is  the  value   of 


_5 

##.  What  is  the  value   of   Tjr 

"" 

23.  What  is  the  value   of 

o 

~182 

£4.  What  is  the  value   of  -~ 

lo 

I  off? 

25.  What  is  the  value   of      gi 

I  off? 

26.  What  is  the  value   of  J  of  i|" 

I  of  f  of  4? 
£7.  What  is  the  value   of       g  x  | 

i  +  3£? 
#S.  What  is  the  value   of  52  _  31 

16*  +  3fo 
#0.  What  is  the  value   of  1^|  _j_  4j" 

30.  What  are  the  daily  wages  of  a  man  who  receives  $14  J  for 
3J  days  work? 

31.  How  many  bushels  of  wheat  at  $f  per  bushel  can  be 
bought  for  $6f  ? 

£2.  How  many  tons  of  coal  at  $4£  can  be  bought  for  $25^  ? 
S3.  At  $1^  per  yard,  how  many  yards  can  be  bought  for  $6^j? 

34.  If  2J  tons  of  hay  cost  $20,  what  will  1  ton  cost? 

35.  I  sold  wheat  at  90c  per  bushel  and  gained  J  of  what  it 
cost.  Find  the  cost  per  bushel. 

EXPLANATION.—  Let  %  =  the  cost.    Then  %  of  the  cost  =  90c  and  % 
of  the  cost  =  90  +  6  =  15c  and  %  or  the  cost  =  5  X  15  =  75c. 

36.  I  sold  a  cow  for  $27  and  lost  TV  of  the  cost.     Find  the 
cost  of  the  cow. 

37.  A  man  bought  a  horse  for  $80,  and  a  buggy  for  f  as  much 
as  the  horse.    The  buggy  cost  If  times  as  much  as  the  harness. 
Find  the  cost  of  the  harness. 

ORAL  REVIEW  PROBLEMS 

1.  What  is  J  of  14?  21?  36?  75?  125? 

2.  What  is  f  of  24?  36?  48?  54?  63? 


»68  NEW   BUSINESS   ARITHMETIC 

8.  What  is  I  of  28?  42?  56?  64?  81? 

4.  18  is  J  of  what  number?  J?  i?  J?  J? 

5.  12  is  |  of  what  number?  f?  f ? 

6.  Count  by  2J  to  100 ;  by  3£ ;  by  6J ;  by  6} ;  by  12J ;  by  16§. 
NOTE. — Practice  on  this  daily  until  it  can  be  done  rapidly  and  accu- 
rately. 

7.  The  sum  of  two  numbers  is  12J,  one  of  the  numbers  is 
7J,  what  is  the  other  number? 

8.  J  of  16  is  J  of  what  number? 

9.  |  of  24  is  J  of  what  number  ? 

10.  A  has  $12£,  B  has  3  times  as  much  as  A  and  C  has  -J  as 
much  as  A  and  B  have.    How  maji^  dollars  have  all? 

11.  At  3  for  4  cents,  how  ma%  pears  can  be  bought  for  20 
cents?  )| 

12.  At  5  for  2  cents,  how  many  apples  can  be  bought  for  30 
cents  ? 

IS.  If  5  bushels  of  oats  cost  $1.25,  what  will  7  bushels  cost? 
14-  A  boy  spent  f  of  his  money  and  had  $12|  left,  how  many 
dollars  had  he  at  first  ? 

15.  Paid  $3J  for  a  pair  of  shoes  and  had  J  of  my  money  left, 
how  much  had  I  at  first? 

16.  A  has  J  of  his  sheep  in  one  pasture,  J  in  another  and  the 
balance,  60  in  a  third  pasture,  how  many  sheep  had  he  in  all? 

17.  A  buys  20  apples  at  2  for  4c  and  30  more  at  2  for  6c.    He 
sells  them  all  at  the  rate  of  4  for  lOc.     Does  he  gain  or  lose  and 
how  much? 

18.  If  5  men  can  dig  a  trench  in  16  days,  what  part  can  3  men 
-dig  in  8  days? 

Find  the  quotient  of: 

19.  T\  -5-  3.  25.  iV  *  14.  81.  12  •*-  TV  37.  30  -^  |. 

20.  H  -*-  6.  26.  V-  +  4.  82.  15  +  }.  S3.  f  -*•  8. 

21.  H  +  7.  27.  if  -5-  10.  33.  25  -5-  2j.  59.  i  -J-  J. 
00.  TT  -5-  5.  03.  6  -*-  f .  84.  18  -*•  |.  40.  f  •*-  f. 
£3.  4  -*-  6.  £0.  8  -f-  4.  35.  f  -i-  15.  ^.  |  •*  A- 
&* -  T\  -*•  15.  50.  9  •*-  i3T.  36.  24  -f-  1.  40.  |  -f-  f. 


FRACTIONS  69 

48.  f  -7-  1.  47.  t  -7-  I.  51.  I  -  |.  55.  TV  *  i 

44.  16  -7-  |.  48.  f  -7-  f .  52.  f  -  TV  5(5.  4-7-9. 

45.  1  -5-  9.  49.  12  -T-  f  53.  f  -5-  If.  57.  15  -  f. 

46.  j\  -  3.  50.  7-|.  54.  4  -  |.  58.  24  -f-  f . 

59.  What  will  12  pounds  of  tea  cost  at  f  dollars  per  pound? 

60.  What  will  -f$  of  a  ton  of  hay  cost  at  $18  per  ton  ? 

61.  Find  the  product  of  J,  J,  ^,  ^  and  J. 

62.  f  is  what  part  of  £? 

63.  If  a  horse  eats  f  bushel  of  oats  in  a  day,  how  long  will  30 
bushels  last  him? 

64.  A  crock  of  butter  weighs  8J  pounds,  and  the  crock  alone 
weighs  1J  pounds.    What  is  the  value  of  the  butter  at  12  J  cents 
per  pound?  ty 

65.  What  will  9f  cords  of  wood  cost  at  4-J  dollars  per  cord? 

66.  At  36  bushels  to  the  acre,  what  is  the  yield  of  if  acres? 

67.  A  lady  bought  5|  yards  of  silk  for  8f  dollars,  what  was 
the  price  per  yard? 

68.  At  If  dollars  per  yard,  how  much  cloth  can  be  purchased 
for  $14  ? 

69.  Sold  a  book  for  $2.25  and  gained  f .    What  did  the  book 
cost  me? 

70.  At  $4.50  per  week,  what  will  five  days'  board  cost? 

71.  Find  the  cost  of  f  of  a  ton  of  coal  at  $6.50  per  ton. 

72.  Find  the  cost  of  f  of  a  yard  of  silk  at  $.60  per  yard. 

73.  A  couch  is  worth  $9.     For  how  much  must  it  be  sold  to 
gain  T3«  ? 

74.  At  1J  dollars  per  day  of  10  hours,  what  will  a  man  earn 
in  7-J  hours? 

75.  If  10  bushels  of  apples  will  make  32  gallons  of  cider,  how 
much  cider  will  7  bushels  make  ? 

76.  Find  the  cost  of  J  of  a  piece  of  cloth  of  36  yards  at  1J  dol- 
lars per  yard. 

77.  A  lady  paid  f  of  J  of  her  money  for  a  dress  and  ^  of  f  of 
it  for  a  cloak.    What  part  of  her  money  did  she  spend  ? 

78.  At  60c  a  dozen  what  is  the  cost  of  %  of  £  of  a  dozen  of 
oranges  ?    What  is  the  cost  of  one  orange  ? 


70  NEW   BUSINESS   ARITHMETIC 

79.  How  many  strips  of  carpet  f  yard  wide  can  be  cut  from  a 
strip  9  yards  wide? 

80.  John  has  $72  in  the  bank.     He  draws  out  TV  of  it  each 
week  for  four  weeks.     How  much  has  he  left? 

81.  A  farmer  sold  10  doz.  eggs  at  16  Jc  a  dozen  and  took  his 
pay  in  sugar  at  5Jc  a  pound.    How  many  pounds  of  sugar  did  he 
.get? 

S2.  What  is  the  cost  of  16  pounds  of  coffee  at  20Jc  per  pound  ? 
'24  Ibs.  of  sugar  at  6fc  per  pound?  12  Ibs.  of  rice  at  5Jc  per  pound? 
--J  barrel  of  flour  at  $6.44  per  barrel?  20  pounds  of  oatmeal  at  9^c 
-per  pound  ?  a  12|  pound  ham  at  10|c  per  pound  ? 

REVIEW    PROBLEMS. 

110.  1.  Reduce  if  If  to  its  lowest  terms. 

2.  Reduce    -f    to  a  fraction  having  27  for  its  denominator. 

3.  Reduce  428|  to  an  improper  fraction. 

4.  Change  -H}1-  to  a  whole  or  mixed  number. 

5.  Reduce  f,  ^,  f  and  f  to  their  least  common  denominator, 

6.  Add  4J,  1  and  f 

7.  Add  23f,  14f,  16f  and  1J. 

8.  Subtract  4£  from  6f. 

9.  Find  the  difference  between  f  of  of  and  J  of  2J. 

10.  The  less  of  two  numbers  is  326f  and  the  greater  is  749^; 
what  is  their  difference? 

11.  Find  the  difference  between  3  X    |   X  f  X  5|  and  3*  X 
I  X  4  X  f . 

12.  Divide  2f  by  TV 

13.  Divide  125f  by  4|. 

14.  A  teacher  who  received  $75  for  a  month's  work,  paid  $17J 
for  board,  $lf  for  light  and  $9T72  for  clothes.    How  much  did  he 
have  at  the  end  of  the  month? 

15.  Find  the  sum  of  23f ,  6,  ||  and  f  of  f . 

16.  How  many  days^must  a  boy  work  to  receive  $12J  if  he  re- 
•ceives  $1J  per  day? 

17.  A  spent  f  of  his  money  and  lost  T3^  of  his  money,  and 
then  had  $21.    How  much  did  he  have  at  first? 


FRACTIONS  71 

18.  John  is  18  years  old,  and  his  age  is  f  of  his  sister's  age. 
How  old  is  his  sister? 

19.  A  speculator  paid  $6428f  for  135J  acres  of  land.     How 
much  did  it  cost  him  per  acre  ? 

20.  I  sold  |  of  a  flock  of  18  sheep  for  $26f .     What  was  the 
price  per  head  for  the  sheep? 

21.  A  has  $40  which  is  1£  times  B's  money.     How  many 
dollars  has  B  ? 

22.  I  bought  three  pieces  of  carpet  at  $1J  per  yard.     One 
piece  contained  40J  yards,  another   33J  yards,  the  other  35T% 
yards.    What  was  the  entire  cost? 

23.  A  merchant  bought  9  dozen  eggs  at  $J  per  dozen  and  paid 
for  them  in  cloth  worth  $f  per  yard.     How  many  yards  of  cloth 
did  it  require? 

24-  The  product  of  two  fractions  is  f ,  and  one  of  the  fractions 
is  {.  What  is  the  other  fraction  ? 

25.  If  the  dividend  is  {^  and  the  divisor  is  f,  what  is  the  quo- 
tient? 

26.  If  2£  barrels  of  flour  cost  $26i,  what  will  8J  barrels  cost? 

27.  A  and  B  worked  for  a  certain  sum.     A  worked  4£  days 
and  received  $6j.     How  much  did  B  receive  if  he  worked  5§ 
days  at  the  same  rate? 

28.  A  farmer  sold  £  of  his  sheep  to  one  man  and  J  to  another, 
when  he  found  that  he  had  140  sheep  left.    How  many  had  he  at 
first? 

89.  A  bought  150  tons  of  hay.  He  sold  35  tons  at  $4f  per 
ton,  40  tons  at  $5J  per  ton  and  f  of  the  remainder  at  $5-J  per  ton. 
How  much  money  did  he  receive? 

30.  How  many  yards  of  cloth  at  $|  per  yard  must  be  given 
for  15  tons  of  coal  at  $4J  per  ton? 

31.  In  how  many  days  will  3  horses  eat  4J  bushels  of  oats  if 
each  horse  eats  \-  of  a  bushel  each  day? 

32.  How  many  pounds  of  butter  at  $T3e  per  pound  will  pay 
for  48  bushels  of  corn  at  $f  per  bushel  ? 

33.  A  man  paid  $3500  for  a  farm  and  this  was  2£  times  the 
cost  of  the  house  which  he  built  upon  it.     Find  the  cost  of  the 
farm  and  house  together. 


72  NEW   BUSINESS   ARITHMETIC 

34.  With  $lf  I  bought  |  of  f  of  f  of  a  yard  of  cloth.  At  that 
rate  what  will  3  yards  cost? 

85.  A  merchant  paid  $25  for  50  gallons  of  molasses.  He  lost 
£  by  leakage  and  sold  20  gallons  at  $f .  The  remainder  was 
sold  so  as  to  gain  $5  on  the  whole.  Find,  the  selling  price  per 
gallon. 

36.  How  many  yards  of  cloth  £  yards  wide  will  line  23J  yards, 
1£  yards  wide  ? 

37.  A  speculator  bought   367£  bushels   of  wheat  at    $f  per 
bushel;  he  sold  126f  bushels  at  $f  per  bushel.     He  afterwards 
bought  260  bushels  at  $|  per  bushel,  and  then  sold  all  he  had  at 
$H  per  bushel.     What  did  he  gain  ? 

88.  A  and  B  own  280  horses.  How  many  horses  does  each 
own,  if  B  owns  f  as  many  as  A  ? 

39.  If  llf  bushels  of  apples  cost  $4T7¥,  what  will  be  the  cost 
of  19^  bushels? 

40.  A  stone  mason  worked  11|  days,  and  after  paying  his 
board  and  other  expenses  with,,|  of  his  earnings,  he  had  $20  left. 
How  much  did  he  receive  a  day? 

41.  What  will  3T9o  acres  of  land  cost,  if  6|  acres  cost  $807? 

42.  How  many  yards  of  carpet  f  yards  wide  will  it  require  to 
carpet  a  room  7J  yards  long  and  4  yards  wide? 

43.  A  and  B  together  have  $364.    B's  money  is  equal  to  f  of 
A's.    How  many  dollars  has  each? 

44»  Lyman  can  do  a  piece  of  work  in  4  days  and  Farwell  can 
do  it  in  5  days.  How  long  will  it  take  them,  working  together,  to 
doit? 

45.  S.  P.  Bruce  bought  40f  acres  of  land  at  $164  per  acre. 
He  sold  25J  acres  to  James  Collins  at  $22J  per  acre,  and  sold  the 
remainder  to  D.  E.  White  at  $15T7¥  per  acre.     How  much  did 
Bruce  pay  for  the  land,  how  much  did  he  receive  for  it,  and  what 
was  his  gain? 

46.  A  can  do  a  piece  of  work  in  10  days ;  B,  in  15  days ;  C,  in 
12  days.    How  long  will  it  take  them  all  to  do  the  work  ? 

47.  A  gentleman,  having  271J  acres  of  land,  sold  J  of  it,  and 
gave  §  of  it  to  his  son.    What  was  the  value  of  the  remainder  at 

per  acre? 


FRACTIONS.  73- 

48.  A  post  stands  J  in  the  mud,  J  in  the  water,  and  21  feet 
above  the  water ;  what  is  its  length  ? 

49.  A  and  B  together  bought  680  sheep.     A  paid  $9  as  often 
as  B  paid  $8.    How  many  sheep  should  each  receive? 

50.  Smith  owning  f  of  a  mill,  sold  f  of  his  share  to  Brown 
for  $870.     Find  the  value  of  the  entire  mill  and  Smith's  share  at 
present. 

51.  How  many  days  will  be  required  for  A,  B  and  C  to  do  a 
piece  of  work,  if  A  can  do  it  in  20  days ;  B  in  30  days ;  C  in  25 
days? 

52.  A  and  B  together  can  do  a  piece  of  work  in  4  days.     A 
can  do  it  alone  in  6  days.    How  long  will  it  take  B  to  do  it  alone  ? 

53.  A  partnership  business  realized  a  profit  of  $6160.     What 
was  each  partner's  gain,  if  A  invested  f  of  the  capital;  B,  T6T; 
C,  the  remainder? 

54.  I  sold  two  horses  for  $240.    The  selling  price  of  one  was 
f  of  the  selling  price  of  the  other.    Find  the  selling  price  of  each 

horse. 

55.  A  dealer  sold  two  cows  for  $24  each.     He  lost  J  of  the 
cost  on  one  and  gained  -J  of  the  cost  of  the  other.     Did  he  gain 
or  lose  and  how  much  by  the  transaction? 

56.  A.  C.  Lamb  bought  a  horse,  buggy  and  harness.     The 
cost  of  the  horse  was  1^  the  cost  of  the  buggy,  and  the  cost  of 
the  harness  was  f  the  cost  of  the  buggy.    What  was  the  cost  of 
each,  if  the  cost  of  the  harness  was  $30  ? 

57.  A's  money  is  £  of  B's  money;  B's  money  is  f  of  Cs 
money;  C's  money  is  If  times  D's  money.     How  much  money 
has  each,  if  f  of  A's  money  is  $64?    How  much  have  they  to- 
gether ? 

58.  How  many  times  is  J  of  f  of  27  contained  in  £  of  J  of 
42|? 

59.  A  and  B  together  own  792  cows ;  f  of  A's  number  equals 
|  of  B's  number.    How  many  cows  does  each  own? 

60.  A  father  left  his  eldest  son  f  of  his  estate,  his  youngest 
son  f  of  the  remainder,  and  his  daughter  the  remainder,  who  re- 
ceived $1723f  less  than  the  youngest  son ;  what  was  the  value  of 
the  estate? 


DECIMAL  FRACTIONS 

111.  A  Decimal  Fraction  is  one  which  has  for  its  denom- 
inator 10,  100,  1000,  or  1  with  any  number  of  ciphers  annexed, 
as  TQ,  Tinr,  -rllhr- 

112.  Common  Fractions  arise  from  dividing  a  unit  into  any 
number  of  equal  parts  as  halves,  thirds,  fifths,  etc. 

Decimal  fractions  arise  from  dividing  a  unit  into  ten  equal 
parts  called  tenths ;  each  of  these  parts  may  be  divided  again  into 
ten  equal  parts  called  hundredths,  etc. 

113.  Since  the  denominator  of  a  decimal  fraction  is  always 
1   with   ciphers   annexed,   it  may   be   expressed   by   writing  the 
numerator  only  and  using  the  decimal  point  to  indicate  the  de- 
nominator. 

114.  The  Decimal  Point  is  a  period  (.)  which  must  always 
be  placed  at  the  left  of  the  decimal.     It  is  read  "and."    Thus  7.4 
is  read  7  and  4  tenths. 

A  number  containing  an  integer  and  decimal  is  called  a  mixed 
decimal. 

115.  Decimal  fractions  like  simple  numbers  increase  in  value 
from  right  to  left  and  decrease  from  left  to  right.    The  first  figure 
on  the  right  of  the  decimal  point  is  called  tenths,  the  second 
hundredths,  the  third  thousandths,  etc. 

Thus, 

jV  is  expressed  .1  and  read  one  tenth. 
T^TTT  is  expressed  .01  and  read  one  hundredth. 
Ter1oTT  is  expressed  .001  and  is  read  one  thousandth. 
"rWir  is  expressed  .125    and    read    one    hundred  twenty-five 
thousandths. 

lOOyffo  is  expressed  100.025  and  is  read  one  hundred,  and 
twenty-five  thousandths. 

NOTE. — Decimal  fractions  are  usually  called  decimals,  and  common 
fractions  merely  fractions. 

74 


DECIMAL   FRACTIONS 


75 


The  relation  of  the  decimals  and  integers  to  each  other  is 
clearly  shown  by  the  following : 

, NUMERATION  TABLE 


1 
=           i 

S2         tn 

a    »•        o   "2 

E      S             rS      3      «<> 
•      .2             "V      ^     -3      c/j 

<U        .*72          5          w          ®          5          "^ 

•S    e    1    -S    f    3   -s   ,< 

^•C^GiSC^ 
3         53       •«         3         41       ^         3 

i  1  1 

housandths. 
sn-thousandths. 
undred-thousand 
illionths. 

m-millionths. 

43 

c 
_o 

1 

u 

c 

KH^ffiH^ffiH 

£     H     ffi 

^     H     ffi     ^ 

(_i 

ffi 

08765432 

1.      2    '  3 

4567 

8 

9 

INTEGERS 

DECIMALS 

By 


examining  this  table  we  see  that 

Tenths  are  expressed  by  one  figure. 

"    two  figures. 


Hundredths 
Thousandths 
Ten  thousandths 


three  figures, 
four  figures. 


COMPARATIVE  VALUES 


Common  Fraction 


Decimal  Fraction 

.5 

.3i  or  .331 

.6f  or  .66| 

.25 

.5  or  .50 

.75 

.2  or  .20 

A 

.6 

.8 

.16f 

.331 

.50 

.66f 

.831 


Common  Fraction 


TV 

A 


Decimal  Fraction 

.14f 

.12i  or  .125 

.25 

.37i  or  .375 

.50 

.62*  or  .625 

.75 

.871-  or  .875 

.Hi 

.1 

.08J  or  .0833i 

.06J  or  .0025 

.05 

.04 


76  NEW    BUSINESS   ARITHMETIC 

From  the  foregoing  we  have  the  following: 
To  Write  Decimals 

a.  Fix  the  decimal  point. 

b.  Write  the  figures  so  that  as  many  places  arc  occupied  at  the 
right  of  the  decimal  point  as  the  decimal  requires. 

NOTE. — In  case  there  are  not  enough  figures  to  occupy  all  of  the 
places  of  the  decimals,  ciphers  must  be  prefixed  to  fill  up  the  vacant 
orders. 

Write  the  following  in  figures: 

1.  Nine-tenths.  4-  Twenty-seven  hundredths. 

2.  Six-tenths.  5.  Ninety  hundredths. 

3.  Four  hundredths.  6.  Three  thousandths. 

7.  Two  hundred  sixty-nine  thousandths. 

8.  Two  hundred,  and  sixty-nine  thousandths. 

9.  Two  hundred  sixty,  and  nine  thousandths. 

10.  Eight  ten-thousandths. 

11.  Forty-one  ten-thousandths. 

12.  Forty,  and,  one  ten-thousandth. 

13.  Six  hundred  thirty-four  ten-thousandths. 

14-  Six  hundred,  and  thirty-four  ten-thousandths. 

15.  Six  hundred  thirty,  and  four  ten-thousandths. 

16.  Three  thousand  four  ten-thousandths. 

17.  Nine  thousand,  and  six  ten-thousandths. 

18.  Sixteen  hundred  thousandths. 

19.  Eighty-two  hundred-thousandths. 

20.  Eighty,  and  two  hundred  thousandths. 

To  Read  Decimals 

Read  the  decimal  as  a  whole  number,  and  then  add  the  name 
of  the  right  hand  order  of  the  decimal. 

How  many  figures  are  required  to  express, 

1.  Tenths?  3.  Thousandths?  5.  Millionths? 

2.  Ten-thousandths?  4-  Hundredths?   6.  Hundred-thousandths? 

What  is  the  name  of  the  decimal  expressed  by 

7.  Two  figures?         9.  One  figure?          11.  Six  figures? 

8.  Four  figures?      10.  Three  figures?     12.  Five  figures? 


DECIMAL   FRACTIONS  77 

Read  the  following: 


13. 

.7 

20. 

.006 

27. 

.27948 

34. 

7.9 

14. 

.04 

21. 

.207 

28. 

.00624 

35. 

9.06 

15. 

.29 

22. 

.190 

29. 

.79250 

36. 

15.248 

16. 

.16 

23. 

.0205 

30. 

.146003  - 

37. 

268.1047 

17. 

.77 

24. 

.1628 

31. 

.020378 

38. 

100.00001 

18.  .019  25.     .9247  32.  .9623479  39.     940.03068 

19.  .234  26.  .02045  33.  .1094682  40.  362.006242 

REDUCTION  OF  DECIMALS 

116.  Reduction  of  Decimals  consists  in  changing  their  form 
without  altering  their  value. 

117.  To  reduce  a  common  fraction  to  a  decimal. 
1.     Reduce  f  to  a  decimal. 

SOLUTION 


or, 

4)3.00 
.75 
We  therefore  have  the  following  rule  : 

To  Reduce  a  Common  Fraction  to  a  Decimal 

a.  Annex  ciphers  to  the  numerator  and  divide  by  the  denomi- 
nator. 

b.  Point  off  as  many  decimal  places  in  the  result  as  there  are 
ciphers  annex  -ed  to  the  numerator. 

NOTE.  —  If  there  continues  to  be  a  remainder  and  the  division  will  not 
end,  the  result  is  called  a  repeating  decimal,  and  the  number  repeated  is 
called  a  rcpetend. 

2.  Reduce  f  to  a  decimal.  7.  Reduce  if  to  a  decimal. 

3.  Reduce  f  to  a  decimal.  8.  Reduce  A  to  a  decimal. 

4.  Reduce  J  to  a  decimal.  9.  Reduce  &•  to  a  decimal. 

5.  Reduce  if  to  a  decimal.  10.  Reduce  JW  to  a  decimal. 

6.  Reduce  ^  to  a  decimal.  11.  Reduce  T*5  to  a  decimal. 
12.  Reduce  -gt^  to  a  decimal. 

IS.  Reduce  12f  to  a  mixed  decimal. 


78  NEW   BUSINESS   ARITHMETIC 

14-  Reduce  42T36  to  a  mixed  decimal. 

15.  Reduce  200*Jv  to  a  mixed  decimal. 

118.  To  reduce  a  decimal  to  a  common  fraction. 

I.  Reduce  .25  to  a  common  fraction0 

SOLUTION 

.25  ==  T2A  =  i 

We  may  give  the  following  rule : 

To  Reduce  Decimals  to  Common  Fractions 

a.  Omit  the  decimal  point,  and  express  the  denominator  of  the 
fraction. 

b.  Reduce  the  fraction  to  its  lowest  terms. 

2.  Reduce  .5  to  a  common  fraction. 

3.  Reduce  .45  to  a  common  fraction. 

4.  Reduce  .125  to  a  common  fraction. 

5.  Reduce  .375  to  a  common  fraction. 

6.  Reduce  .016  to  a  common  fraction. 

7.  Reduce  .075  to  a  common  fraction. 

8.  Reduce  .625  to  a  common  fraction. 

9.  Reduce  .9375  to  a  common  fraction. 
10.  Reduce  .0008  to  a  common  fraction. 

II.  Reduce  28.0625  to  a  mixed  number. 
12.  Reduce  136.005  to  a  mixed  number. 
18.  Reduce  .44$  to  a  common  fraction. 

14.  Reduce  .142857-f  to  a  common  fraction. 

15.  Reduce  .0833  J  to  a  common  fraction. 

16.  Reduce  .0053f  to  an  equivalent  common  fraction. 

17.  Reduce  107.166J  to  an  equivalent  mixed  number. 

18.  Reduce  8.123f  to  an  equivalent  mixed  number. 

19.  What  mixed  number  is  the  equivalent  of  16.0483J? 

20.  What  mixed  number  is  the  equivalent  of  143.42H? 


DECIMAL   FRACTIONS  79 

ADDITION   OF   DECIMALS 

119.  1.  Find  the  sum  of  13.25,  .637,  142.6,  .085  and  4.2631. 

SOLUTION 

13.25 

.637 
142.6 

.085 
4.2631 
260.8351 

From  the  foregoing  we  have  the  following: 

To  Add  Decimals 

a.  Write  the  numbers  so  that  figures  of  the  same  order  are  in 
the  same  column,  with  the  decimal  points  in  a  column. 

b.  Add  the  same  as  in  whole  numbers  and  place  the  decimal 
point  in  the  result  directly  under  the  decimal  points  above. 

Find  the  sum  of  each  of  the  following : 

(2)  (3)  (4)  (5)  (6) 

.1625  +  .2314  +  .1847  +  5.6  +  12.70  ==  x 

.3284  +  .3162  +  .3426  +  .853  +  7.28  =  x 

.2341  +  .3456  +  2.561  +  17.928  +  .785  =  x 

.3213  -f  .2125  +  4.125  +  .0035  +3.  =  x 

.4234  +  .4213  +  5.207  +  21.15  +  .095  =  x 

x  +     x  +  x  +  .r  -f  x  =  x 

7.  21.75,  8.9,  148.273  and  269.412. 

8.  328.013,  93.6,  80.003  and  964.24. 

9.  4.5,  49.65,  146.234  and  9268.1726. 

10.  200.002,  920.046,  76.36  and  95.1074. 

11.  12.60.9,  5394.08,  675.149    and  260.024. 

12.  Add,   thirty-seven,   and   three   hundredths;   five   hundred 
twenty-one  thousandths;  nine-tenths;  one  thousand;   four  thou- 
sand, and  four  ten-thousandths. 

13.  What   is   the   sum   of   twenty-six,    and    twenty-six   hun- 
dredths ;  seven-tenths ;  six,  and  eighty-three  thousandths ;  four, 
and  four-thousandths? 


80  NEW   BUSINESS   ARITHMETIC 

14-  What  is  the  sum  of  twenty-eight,  and  seven-tenths;  one 
hundred  forty,  and  sixteen  thousandths;  thirty-seven  ten-thou- 
sandths ;  twenty-five,  and  fifteen  hundred-thousandths ;  four,  and 
eight  hundredths  ? 

15.  How  many  yards   in  four   pieces  of  cloth,  the  first  con- 
taining 28.375  yards;  the  second  26.4635  yards;  the  third  14.05 
yards,  and  the  fourth  18.2  yards? 

16.  A  boy  paid  $8.40  for  a  coat,  $3.65  for  a  vest,  $6.152  for  a 
pair  of  pants,  $4  for  a  hat  and  $2.857  for  a  pair  of  shoes.    What 
sum  did  he  pay  for  all? 

17.  A  farmer  received  $478.285  for  wheat,  $362.675  for  oats, 
$140  for  rye,  $360.90  for  corn  and  $200  for  barley.     How  much 
did  he  receive  for  all? 

18.  My  farm  consists  of  7  fields,  containing  12}  acres,  18f 
acres,  9  acres,  24J  acres,  4^|  acres,  8T%  acres,  and  15 Jf  acres  re- 
spectively.   How  many  acres  in  my  farm  ? 

NOTE. — Reduce  the  common  fractions  to  decimals  before  adding. 

19.  A   farmer  sold   84£  bushels  of  wheat;   136}  bushels   of 
oats;  122f  bushels  rye;  29.0687  bushels  of  barley;  and  548.365 
bushels  of  corn.     How  many  bushels  of  grain  did  he  sell  in  all? 

20.  A  merchant  sold  3J  yards  of  cloth  for  $4.675 ;  2.5  yards 
of  another  piece  for  $1J;  11}  yards  of  another  piece  for  $6|;  and 
5iV  yards  of  another  piece  for  $-Jf.     How  many  yards  did  he 
sell  in  all,  and  for  how  much? 

21.  Three  hundred  four,  and  thirty-two  thousandths  miles; 
eighteen,  and  two    thousand     seventy-five     hundred-thousandths 
miles;  three,  and  fifteen  ten-thousandths  miles;  and  five  thou- 
sand eighty-two,  and  one  thousand  nineteen  hundred-thousandths 
miles  equal  what? 

22.  A  farmer  owns  five  tracts  of  land  containing  respectively 
eight    hundred    seventy-six,    and    eighteen    thousandths     acres ; 
twenty-eight,  and  seven-tenths  acres ;  four  hundred  fifty-six,  and 
five  hundred  six  ten-thousandths  acres ;  seventy-two,  and  thirteen 
thousandths  acres ;  and  nine  thousand  three  hundred  twenty-four, 
and   seven   hundred   sixteen   hundred-thousandths   acres.      How 
many  acres  of  land  did  the  farmer  own? 


DECIMAL   FRACTIONS  81 


SUBTRACTION  OF   DECIMALS 

120.  1.  From  36.85  take  25.015. 

SOLUTION 

36.85 
25.015 


11.835 

To  Subtract  Decimals 

a.  Write  the  numbers  so  that  figures  of  the  same  onder  are  in 
the  same  column,  with  the  decimal  points  in  a  column. 

b.  Subtract  as  in  whole  numbers,  supposing  any  vacant  places 
on  the  right  of  the  decimal  to  be  filled  by  ciphers,  and  write  the  re- 
sult beneath,  with  the  decimal  point  immediately  under  those 
above. 

Subtract  each  of  the  following: 

(2)            (3)              (4)  (5)                (6) 

.9685         .7568         12.3061  15.02  $14,05 

.7134         .3724           2.1475  7.3481  $     .975 

7.  From  890.78  take  762.165. 

8.  From  1162.847  take  968.28. 

9.  From  9280.175  take  1186.2468. 

10.  From  95.06  take  17.281. 

11.  From  190.004  take  75.86. 

12.  From  $126.28   take   $98.95. 

13.  From  $2680.105  take  $962.189. 

H.  From  16.084  take  2  ten-thousandths. 

15.  From  nine  take  nine  ten-thousandths. 

16.  From  43fjj-  take  75  hundredths. 

17.  From  825  take  .825. 

18.  From  28. 16^  take  17ft- 

19.  From  324.185J  take  218.004J. 

20.  From  128.37|  take  lOO.OOlf . 

21.  3.25       +  32.25  -  30.125         =  x. 
1.001     +       .565  .5625       =  x. 

.2436  +  1.04  .325155  =  x. 

100.0025  +  2.51634  —  70.12     =  x. 

7.05   -f  43.2114  —  14.171432  =  x. 

x    +  x    —  x    =  x. 


82  NEW   BUSINESS   ARITHMETIC 

MULTIPLICATION  OF   DECIMALS 
121.  1.  Multiply  .45  by  .5. 

SOLUTION 

.45  X  .5  =  TVir  X  TV  =  -fffo  =  .225 
or, 
.45 
.5 


.225 

Therefore  we  deduce  the  following: 

To  Multiply  Decimals 

a.  Write  the  numbers  and  multiply  as  in  simple  numbers. 

b.  Point  off  in  the  product  as  many  figures  for  decimals  as 
there  are  decimal  places  in  the  multiplicand  and  multiplier. 

NOTE. — If  the  number  of  figures  in  the  product  is  less  than  the  num- 
ber of  decimals  in  the  multiplier  and  multiplicand,  prefix  ciphers  to  the 
product  sufficient  to  make  it  equal. 

2.  Multiply  72.18  by  .267.  6.  Multiply  2.165  by  2.165. 

3.  Multiply  1.964  by  .1362.  7.  Multiply  96.87  by  .2146. 

4.  Multiply  7.48  by  12.4.  8.  Multiply  140.0165  by  7.37. 

5.  Multiply  18.95  by  16.47.  9.  Multiply  1260.50  by  3.005. 

10.  Multiply  seven-tenths  by   seven-hundredths. 

11.  Multiply  145  by  one  hundred  forty-five  thousandths. 
12*  Multiply    sixty-five    thousandths     by     twenty-three     ten»- 

thousandths. 

13.  Multiply  one  million  by  one  millionth. 

14.  I  sold  127.5  bushels  of  wheat  at  $.8725  per  bushel.    What 
did  I  receive  for  it? 

15.  Find  the  result  of  145.08  X  3.75  X  .003. 

16.  Bought  28.75  tons  of  coal  at  $6.30  per  ton,  and  sold  it  for 
$8.125  per  ton.    How  much  did  I  gain? 


DECIMAL   FRACTIONS  88 

DIVISION   OF   DECIMALS 
±22.  1.  Divide  .125  by  .5. 

SOLUTION 

25 
19,    .     -  _  1^5          5  _  ^        M__  25 

"iooo""  io~~»iwx  /"Too-"'25 

100 
or, 

.5).  125 


Therefore  we  have  the  following: 

To  Divide  Decimals 

a.  Write  the  numbers  and  divide  as  in  integers. 

b.  Point  off  as  many  decimal  figures  from  the  right  of  the 
quotient  as  the  number  of  decimal  figures  in  the  dividend  exceed 
those  in  the  divisor. 

NOTE.  —  If  the  dividend  contains  a  less  number  of  decimal  places  than 
the  divisor,  enough  ciphers  must  be  added  before  beginning  the  operation 
to  make  the  decimal  places  in  the  dividend  equal  those  in  the  divisor. 

2.  If  there  is  a  remainder  after  dividing  the  dividend,  annex  ciphers 
and  continue  the  division.  The  ciphers  annexed  are  decimals  of  the 
dividend. 

2.  Divide  .675  by  .15.  7.  Divide  53.105  by  247. 

3.  Divide  $17.48  by  3.8.         8.  Divide  12948  by  1.56. 

4.  Divide  3.822  feet  by  .49.   9.  Divide  $4608  by  $9.6. 

5.  Divide  .6345  by  .027.       10.  Divide  691.92  by  .0372. 

6.  Divide  2.016  by  24.          11.  Divide  5312.5  ft.  by  12.5  ft. 

12.  Divide  .50328  by  .1864. 

13.  Divide  589745  yards  by  27.43  yards. 

14-  How  many  times  is  .7854  contained  in  12? 

15.  What  is  the  result  of  9  divided  by  450? 

16.  At  $.73  per  bushel,  how  many  bushels  of  ;corn  can  I  buy 
for  $1058.50? 

17.  At  $22.40  each,    how    many    sewing    machines    can    be 
bought  for  $716.80? 


84  NEW  BUSINESS  ARITHMETIC 

18.  Divide  fifteen,  and  eight  hundred  seventy-five  thousandths, 
by  twenty-five  ten-thousandths. 

19.  Divide  thirty-seven,  and  five  thousand  six  hundred  four- 
teen ten-thousandths  by  two  hundred  eighteen  millionths. 

20.  Divide  forty-five,  and  three-tenths  by  fifteen  thousandths, 

REVIEW   PROBLEMS 

123.  1.  Add  twenty-five  thousandths;  nineteen,  and  one 
hundred  forty-six  ten-thousandths;  four-tenths;  nine,  and  twen- 
ty-seven hundredths ;  thirteen,  and  forty-five  millionths ;  sixty- 
four,  and  nine  hundredths;  sixteen,  and  three-tenths. 

2.  What  is  the  sum  of  81.003  +  5000.4  +  5.0008  +  73.87563 
+  1000  +  25  +  3.000548  +  .0315? 

3.  A  farmer  has  three  fields;  the  first  has  247.125  acres,  the 
second  128.375  acres,  and   the   third    197.5   acres.     How   many 
acres  has  he  ? 

4.  Find  the  sum  of  $28.45,  $92.32,  $84.23,  $174.125,  $262.25, 
$890.625  and  $148. 

5.  I    received    from   A   $168.95,    from    B    $365.70,    from    C 
$640.20.    I  paid  D  $212.45,  E  $312.27,  and  F  $126.09.    How  much 
had  I  left? 

6.  From  one  hundred  twenty-five,  take  one  hundred  twenty- 
five  ten-thousandths. 

7.  What  is  the  difference    between    one    million    and    one- 
millionth  ? 

8:  Multiply  :425  by  .23. 

9.  Multiply  36.005  by  20.007. 

10.  A  merchant  bought  7  pieces  of  muslin  of  36.75  yards  each 
at  $.065  per  yard,  9  pieces  of  flannel  of  42.08    yards    each    at 
$.1275  per  yard,  15  pieces  of  drilling  of  52.4  yards  each  at  $.092 
per  yard.    What  was  the  cost  of  all? 

11.  Divide  .275  by  800. 

12.  Divide  1.652  by  .236. 
IS.  Divide  2.39015  by  .007. 

14.  If  flour  is  worth  $6.475  per  barrel,  how  many  barrels  can 
be  bought  for  $692.825? 

15.  Reduce  .875  to  a  common  fraction. 


COMPOUND   NUMBERS  85 


16.  Reduce  146.0625  to  a  mixed  number. 

17.  Reduce  2!^  to  a  decimal. 

If3 

18.  Reduce  -    r  to  a  decimal. 


19.  A  farmer  sold  7  loads  of  grain,  each  load  containing  46f 
bushels,  at  62f  cents.    What  did  he  receive  for  the  entire  quantity 
of  grain  ? 

20.  How  many  times  will  .05  of  17.875  be  contained  in  .25 
of  12f? 


COMPOUND   NUMBERS 

124.  A  Denominate  Number  is  a  concrete  number  which 
expresses  a  particular  kind  of  quantity;  as  3  feet,  o  pounds. 

125.  A   Compound  Denominate  Number  is  one  which  ex- 
presses a  quantity  in  different  names,  but  of  the  same  kind,  as  3 
feet  4  inches ;  5  pounds  7  ounces. 

All  denominate  numbers  may  be  embraced  under  the  follow- 
ing divisions :  Value,  Weight,  Measure  and  Time. 

126.  Value  is  the  property  of  an  article  which  renders  it 
useful. 

Value  is  of  three  kinds :    Intrinsic,  Commercial  and  Nominal. 

127.  Intrinsic  Value  is  that  which  is  inherent  in  the  article, 
usually  measured  by  the  labor  necessary  to  produce  the  article. 

128.  Commercial  Value  is  the  value  at  which  an  article  will 
exchange   for  other  articles   in  the  markets,   or   its   purchasing 
power. 

129.  Nominal  Value  is  that  which  is  named  or  placed  upon  an 
article. 

In  all  civilized  countries  commercial  value  is  measured  in 
money. 

130.,  Money  is  a  measure  of  value,  and  the  medium  of  ex- 
change in  business  transactions.  It  usually  consists  in  stamped 
metals  called  coin,  and  printed  bills  or  notes  called  currency. 


UNITED   STATES   MONEY 

131.  United  States  Money  is  the  legal  currency  of  the  United 
States.    Its  denominations  increase  and  decrease  upon  a  decimal 
scale,  ten  units  of  one  order  making  one  of  the  next  higher. 

The  dollar  is  the  unit,  and  the  decimal  point  or  period  is  used 
to  separate  dollars  from  the  cents  and  mills. 

132.  The  Coin  of  the  United  States  consists  of  gold,  silver, 
nickel  and  bronze. 

The  Gold  Coins  are  the  double-eagle,  eagle  and  half-eagle 
pieces. 

The  Silver  Coins  are  the  dollar,  half-dollar,  quarter-dollar  and 
ten-cent  pieces. 

The  Nickel  Coin  is  the  five-cent  piece. 

The  Bronze  Coin  is  the  one-cent  piece. 

The  Paper  Money  of  the  United  States  consists  of  United 
States  treasury  notes,  national  bank  bills  and  gold  and  silver  cer~ 
tificates. 

TABLE 

10  mills    (m.)    make   1   cent ct. 

10  cents  "       1  dime d, 

10    dimes  "       1    dollar $ 

10   dollars  "       1   eagle E. 

NOTE. — 1.  The  mill  is  a  denomination  used  only  in  computations ;  it  is 
not  a  coin. 

2.  The  character  $  is  supposed  to  be  a  contraction  of  U.  S.  (United 
States),  the  U.  being  placed  upon  the  S. 

To  Read  or  Write  United  States  Money 
Read  or  write  the  number  at  the  left  of  the  period  as  dollars^ 
the  first  two  figures  at  the  right  of  the  period  as  cents;  and  if  there 
be  a  third  figure,  as  mills. 
Read  the  following : 
J.  $.16.  Jf.  $  7.35.  7.  $1000.005. 

2.  $.09.  5.  $12.203.  8.  $  478.105. 

3.  $.965.  6.  $10.10.  9.  $  901.0706. 

86 


UNITED   STATES   MONEY  87 

10.  Write  thirty-nine  cents. 

11.  Write  fourteen  cents  and  seven  mills. 

12.  Write  ninety-three  cents  and  four  mills. 

13.  Write  nine  dollars  and  twenty-five  cents. 

14-  Write  one  hundred  forty-six  dollars,  four  cents  and  seven 
mills. 

15.  Write  one  hundred  dollars,  one  cent  and  five  mills. 

16.  Change  375  cents  to  dollars. 

NOTE. — To  change  cents  to  dollars  point  off  two  places. 

17.  In  1367  cents  how  many  dollars? 

18.  In  24367  mills  how  many  dollars? 

NOTE. — To  change  mills  to  dollars  point  off  three  places. 

19.  Reduce  3428  mills  to  dollars. 

20.  In  $36  how  many  cents  ? 

21.  In  $18.25  how  many  cents? 

22.  In  16  cents  how  many  mills? 
28.  In  $235.046  how  many  mills? 
24.  In  $3.005  how  many  mills? 

ADDITION 

133.  1.  What  is  the  sum  of  145  dollars  25  cents;  60  dollars 
30  cents;  18  dollars  10  cents  5  mills;  340  dollars  37£  cents;  and 
12  dollars  87  cents  5  mills? 

SOLUTION 

$145.25 
60.30 
18.105 
340.375 

12.875 
$576.905 

To  Add  United  States  Money 

a.  Write  dollars  under  dollars,  cents  under  cents,  etc. 

b.  Add  as  in  simple  numbers  and  place  the  point  in  the  amount 
as  in  addition  of  decimals. 

2.  Find  the  sum  of  180  dollars  15  cents  7  mills;  236  dollars 
42  cents  4  mills;  105  dollars  65  cents  3  mills;  118  dollars  50 
cents  9  mills ;  300  dollars  4  cents  2  mills. 


88  NEW  BUSINESS  ARITHMETIC 

8.  Find  the  sum  of  65  cents ;  1  dollar  1  cent  1  mill ;  100  dol- 
lars; 32  dollars  10  cents  1  mill;  18  cents  6  mills;  12£  cents;  85 
cents  7  mills. 

4.  A  collector  was  sent  out  to  collect  bills  for  the  following 
amounts:  $128.14;  $36.25;  $10.67^;  $246.34:  $1.62$;  and  $100. 
What  was  the  total  amount  to  be  collected? 

5.  A  lady  made  purchases  as  follows :    A  dress  for  $16.35 ; 
a  hat  for  $9.87|;  a  pair  of  shoes  for  $4.50;  a  paper  of  needles 
for    6    cents ;    some    ribbon    for  35  cents.    What  was  the  total 
amount  of  her  purchases? 

6.  A  merchant  has  due  him  from  one  customer  $536.84 ;  from 
another  $387.25;  from  another  $200.40;  from  another  $230.75; 
from  another  $804.32;  and  from  another  $675.62^.    What  is  the 
total  amount  due  from  these  six  customers? 

7.  A  farmer  paid  $2867.50  for  a  farm.    He  expended  $238.60 
for  fencing  it;  $860.12  for  a  house  upon  it;  and  $216.30  for  other 
improvements.    What  was  the  farm  then  worth  ? 

8.  Bought  a  horse  for  $180.65 ;  a  buggy  for  $212.35 ;  a  har- 
ness for  $30.75,  and  a  saddle  for  $18.60.    Find  the  total  ;cost  of 
the  outfit. 

9.  The  annual  expenses  of  a  business  are,  for  rent  $2000; 
clerk  hire  $3250;  fuel  and  light  $875.30;  advertising  $1632.04; 
insurance  $400;  repairs  $142.80;  incidentals  $126.34.     Find  the 
total  expenses  of  the  business  for  the  year. 

10.  A  bought  a  hat  for  $4.62^;  a  pair  of  shoes  for  $3f ;  an 
umbrella  for  $1J;  a  pair  of  gloves  for  $.62J  and  a  cane  for  $}. 
What  was  the  entire  cost  of  his  purchases? 

11.  A  student  expended  for  tuition  $86.50;  for  board  $138.45; 
for  clothes  $46.32 ;  for  church  and  charity  $11.48.    What  amount 
did  he  expend  in  all? 

12.  A  lady  bought  groceries  to  the  amount  of  $5.80;  meats 
$3.48;   dry   goods   $26.42;   carpets   $148.35;   millinery   $23.62£. 
What  was  the  total  amount  of  her  expenditures? 

IS.  The  expenses  of  a  household  for  one  month  are:  grocer- 
ies $36.40;  meats  $18.60;  coal  $11.30;  kindling  $2.65;  milk 
$9.80;  gas  $3.75;  servant  $4.50;  incidentals  $13.65.  What  are 
the  total  expenses? 


UNITED    STATES    MONEY  89 

SUBTRACTION 

134.  1.  From  123  dollars  75  cents  take  84  dollars  42  cents. 

SOLUTION 

$123.75 

84.42 
$39.33 

To  Subtract  United  States  Money 

a.  Write  the  subtrahend  under  the  minuend,  dollars  under  dol- 
lars and  cents  under  cents. 

b.  Subtract  as  in  simple  numbers  and  place  the  point  in  the  re- 
mainder directly  under  the  point  above. 

2.  From  246  dollars  5  cents  take  134  dollars  17  cents. 

3.  From  100  dollars  1  mill  subtract    16    dollars    25    cents   2 
mills. 

4.  From  1000  dollars  take  1  cent  1  mill. 

5.  John  Davis  owes  1000  dollars  25  cents  4  mills ;  if  he  pay 
832  dollars  16  cents  7  mills,  how  much  will  he  still  owe? 

6.  A   man   bought  a    farm   for   $3625.14   and   sold    it    for 
$4201.70.    What  did  he  gain  by  the  operation  ? 

7.  Having  $6287.35  deposited  in  a  bank  I  drew  out  at  one 
time  $2436.14  and  at  another  time  $900.15.    How  much  had  I  re- 
maining in  the  bank  ? 

8.  A  boy  earned  $79.15.     He  spent  $18.40  for  clothes,  and 
$9.85  for  books.    How  much  had  he  left? 

9.  A  merchant  in  one  week  sold  $1160  worth  of  goods,  and 
paid  of  that  sum  $170  for  rent,  $86  for  light,  $140  for  clerk  hire. 
How  much  had  he  left  ? 

10.  A  gentleman  paid  for  a  lot  $1650,  and  for  a  house  $2000 
more  than  the  lot  cost  him.    He  then  sold  both  house  and  lot  for 
$4627.35.    What  did  he  gain  or  lose  by  the  transaction? 

11.  A  grocer  sold  to  a  customer,  coffee  amounting  to  $1|; 
tea  $2|;  sugar  $.62J;  rice  $.33;  crackers  $J;  cheese  $.90;  bar- 
rel of  salt  $1.35.    He  received  in  payment  a  ten-dollar  bill.    How 
much  change  should  he  return  to  the  customer? 


90  NEW   BUSINESS   ARITHMETIC 

MULTIPLICATION 

135.  1.  If  one  yard  of  cloth  cost  $3.625  what  will  15  yards 
cost? 

SOLUTION 


$54.375 

To  Multiply  United  States  Money 

a.  Multiply  as  in  simple  numbers  and  point  off  the  product  as 
in  multiplication  of  decimals. 

2.  If  one  barrel  of  flour  cost  $6.75  what  will  27  barrels  cost? 

3.  At  $34.25  apiece  what  must  be  paid  for  17  cows? 

4.  A  speculator  bought  a  farm  of  160  acres  at  $45.25  per 
acre.    What  did  the  farm  cost? 

5.  A  merchant  sold  the  following  bill  of  goods :     9  pounds 
of  tea  at  56  cents  a  pound ;   6  pounds  of  butter  at  35  cents  a 
pound ;  8  pounds  of  coffee  at  31  cents  a  pound ;  7  gallons  of  mo- 
lasses at  75  cents  a  gallon.    What  did  the  whole  amount  to? 

6.  A  farmer  sold  125  bushels  of  wheat  at  87-J  cents  per  bushel ; 
243  bushels  of  oats  at  37J  cents  per  bushel;  584  bushels  of  corn 
at  $f  per  bushel  and  48  bushels  of  clover  seed  at  $1.65  per  bushel. 
He  received  in  payment  a  note  for  $200 ;  and  the  balance  in  money. 
How  much  money  did  he  receive? 

7.  Joseph  Brown  bought  a  fruit  farm  consisting  of  35  acres 
for  $6340.    He  sold  21  acres  of  it  for  $5216.87^  and  the  balance 
at  $215.35  per  acre.     What  did  he  gain? 

8.  A  merchant  bought  325  barrels  of  flour  at  $6.75  per  bar- 
rel.   He  sold  210  barrels  at  $7.12-|  per  barrel  and  the  remainder 
at  $6.62^  per  barrel.    How  much  did  he  gain  or  lose  in  the  oper- 
ation ? 


v*° 

OF  ""HE 

UNIVERSITY 

OF  mttTED    STATES    MONEY  91 


DIVISION 

136.  1.  If  27  yards  of  cloth  cost  $9.45,  what  will  one  yard 
cost? 

SOLUTION     , 

27)$9.45(.35 
81 
135 
135 


To  Divide  United  States  Money 

a.  Divide  as  in  simple  numbers  and  point  off  the  quotient  as  in 
division  of  decimals. 

NOTE. — If  the  dividend  will  not  contain  the  divisor  an  exact  number 
of  times,  ciphers  may  be  annexed,  and  the  division  continued  as  in  decimals. 

2.  If  16  pounds  of  tea  cost  $8.96  what  will  one  pound  cost? 

3.  If  25  acres  of  land  cost  $1125,  what  will  1  acre  cost? 

4.  If  36  yards  of  broadcloth  cost    $139.50,    what    will    one 
yard  cost? 

5.  If  45  pounds  of  butter  cost  $14.40  what  will  be  the  cost  of 
1  pound? 

6.  How  many  barrels  of  apples  can  be  bought  for  $534.37^ 
at  the  price  of  $1  -J  per  barrel  ? 

7.  A  man  earns  $864  in  a  year.    How  much  is  that  a  month  ? 

8.  If  100  acres  of  land  cost  $5637.50,  what  will  one  acre 
cost? 

9.  If  265  pounds  of  lard  cost  $34.45,  what  will  one  pound 
cost? 

10.  A  farmer  exchanged  235  bushels  of  corn  at  45  cents  a 
bushel  for  buckwheat  at  85  cents  a  bushel.     How  many  bushels 
of  the  latter  did  he  receive  ? 

11.  A  young  man's  board  for  one  year  is  $318f.    How  much 
is  it  per  day? 

12.  A  grocer  bought  18  kegs  of  butter  of  25  pounds  each  for 
$121.50.     How  much  was  that  per  pound? 

13.  If  16  men  receive  $516  for  43  days'  work,  how  much  does 
each  man  earn  a  day? 

14-  C  earned  $90  in  40  days,  working  10  hours  a  day;  how 
much  did  he  earn  an  hour? 


SHORT  METHODS 


137.  An  Aliquot  Part  of  a  number  is  one  which  will  exactly 
divide  it.  Thus  5,  10  and  20  are  aliquot  parts  of  60;  12}  of  100, 
etc. 

Aliquot  Parts  of  One  Dollar 

V  8}  cents  = 
v  6J  cents  = 
5     cents  = 


50  cents  =  }  of  $1. 
33}  cents  =  }  of  $1. 
25  cents  =  }  of  $1. 
20  cents  =  J  of  $1. 
•^6*  cents  =  J  of  $1. 
12}  cents  =  }  of  $1. 
10  cents  =  TV  of  $1. 


1 

2} 

3} 

2 

5 

6* 

3 

7} 

10 

4 

10 

13} 

5 

12} 

16* 

6 

15 

20 

7 

17} 

23} 

8 

20 

26| 

9 

22} 

30 

10 

25 

33} 

of  $1. 

of  $1. 

of  $1. 

cents  =  §  of  $1. 
vJ  62}  cents  =  f  of  $1. 
si  87}  cents  =  J  of  $1. 
*  83}  cents  =  f  of  $1. 

Multiplication  Table 

6i   8} 
12}  16f 
18*  25 
25   33} 


12} 

16* 

25 

33} 

37} 

50 

50 

66* 

62} 

83} 

75 

100 

87} 

116* 

100 

133} 

112} 

150 

125 

166* 

37}  50 

43*  58} 

50  66* 

56i  75 

62}  83} 

NOTES. — 1.  This  table  can  be  easily  learned  and  will  prove  convenient 
in  mental  operations. 

2.  Black  figures  indicate  multipliers  and  multiplicands.  Intersecting 
points  of  horizontal  and  vertical  columns  give  the  products. 

Count  by  2}  to  100 ;  as,  2},  5,  7},  etc. 

Count  by  12}  to  100,  return  by  subtracting  10's. 

92 


SHORT   METHODS  93 

Count  by  3J  to  100,  return  by  subtracting  5's. 
Count  by  16|  to  100,  return  by  subtracting  12J's. 

138.  To  Hud  the  cost  of  a  quantity  when  the  price  is  an  ali- 
quot part  of  $1. 

1.  Find  the  cost  of  48  pounds  of  butter  at  25  cents  a  pound. 

SOLUTION         EXPLANATION.— At  $1  a  pound  48  pounds  would  cost  $48, 
4)    48          but  25  cents  is  %  of  a  dollar,  and  hence  the  whole  cost  will 
$12          be  %  of  $48  or  $12. 

From  this  solution  we  have  the  following : 
To  Find  the  Cost  When  the  Price  Is  an  Aliquot  Part  of  $1 

a.  Take  such  part  of  the  given  quantity  as  the  price  is  part  of 
one  dollar. 

2.  What  cost  218  gallons  of  syrup  at  50c  per  gallon? 

3.  What  cost  468  yards  of  cloth  at  33 J  cents  per  yard  ? 

4.  What  cost  1250  pounds  of  lard  at  12J  cents  per  pound? 

5.  What  cost  564  dozen  eggs  at  16§  cents  per  dozen? 

6.  What  cost  26840  yards  of  calico  at  8j  cents  per  yard? 

7.  Find  the  cost  of  2435  pounds  of  pork  at  6£    cents    per 
pound. 

8.  What  cost  486  cans  of  peaches  at  20  cents  per  can? 

9.  What  cost  214J  quarts  of  berries  at  5  cents  per  quart? 
10.  At  16|  cents  per  yard,  what  cost  26480  yards  of  linen? 

139.  To  find  the  quantity  when  the  price  is  an  aliquot  part 
of$l. 

1.  If  cloth  costs  33  J  cents  per  yard,  how  many  yards  can  be 
bought  for  $29  ? 

SOLUTION 

At  33^c  per  yard  $1  will  buy  3  yards. 
$29  will  buy  3  X  29  or  87  yards. 

To  Find  the  Quantity  When  the  Price  Is  an  Aliquot  Part  of  $1 

a.  Multiply  the  cost  by  the  quantity  that  can  be  bought  for  one 
dollar. 

S.  If  one  pound  of  butter  cost  25  cents,  how  many  pounds 
can  be  bought  for  $13.25  ? 


94  NEW   BUSINESS   ARITHMETIC 

3.  At  IGf  cents  a  dozen,  how  many  dozen  eggs  can  be  bought 
for  $32.15? 

4.  A   gardener   exchanged    potatoes   worth    66f    cents    per 
bushel  for  5  barrels  of  flour  worth  $6.75  per  barrel.    How  many 
bushels  of  potatoes  did  he  give  ? 

5.  A  farmer  sold  15  bushels  of  buckwheat  at  87J  cents  per 
bushel  and  received  in  pay  pork  at  6J  cents  per  pound.     How 
many  pounds  did  he  receive? 

6.  John  Wilson  expended  $3625  in  the  purchase  of  a  farm  at 
$50  per  acre.    How  many  acres  did  he  buy  ? 

7.  I  exchange  275  feet  of  city  land  worth  $75  per  foot,  for 
farming  land  worth  $66f    per    acre.     How    many    acres    do    I 
receive  ? 

8.  A  grocer  expended  $32.50  for  A  sugar  worth  6^  cents  per 
pound,  and  $48.75  for  C  sugar  at  5  cents  per  pound.    How  many 
pounds  of  sugar  did  he  buy  ? 

140.     To  find  the  cost  of  articles  sold  by  the  100  or  1000. 

NOTE.— C  stands  for  100.     M  stands  for  1000. 

1.  What  is  the  cost  of  1850  feet  of  lumber  at  $3.20  per  C? 

SOLUTION 

1850  feet  ==  18.50  C  feet. 
18.50  X  $3.20  =  $59.20. 

Therefore  we  may  deduce  the  following  rule: 

To  Find  the  Cost  of  Articles  Sold  by  the  C  or  M 

a.  Reduce  the  quantity  to  hundreds  and  decimals  of  a  hundred 
or  thousands  and  decimals  of  a  thousand. 

b.  Multiply  by  the  price  per  C  or  per  M  and  point  off  as  in 
multiplication  of  decimals. 

NOTE. — Use  aliquot  parts  where  practicable. 

2.  Find  the  cost  of  1645  pounds  of  beef  at  $4.60  per  C. 
8.  Find  the  cost  of  4267  pounds  of  scrap  iron  at  $5.30  per  C. 
4.  What  is  the  freight  from  New  York  to  Chicago  on  6238 
pounds  of  merchandise  at  $1.62^  per  C? 


SHORT   METHODS  95 

5.  What  will  be  the  cost  of  2632  feet  of  pine  boards  at  $18,50 
per  M  ? 

6.  What  cost  6428  bricks  at  $6.50  per  M? 

7.  What  will  be  the  cost  of  1625  feet  of  oak  lumber  at  $35 
per  M? 

8.  Find  the  cost  of  384  ax  handles  at  $11.50  per  C. 

9.  Find  the  cost  of  8425  shingles  at  $7.30  per  M. 

10.  A  printer  printed  11267  envelopes  at  $2.15  per  M.    What 
did  he  receive  for  the  job? 

11.  In  repairing  a  house  I  used  2640  bricks  at  $5.80  per  M; 
2180  feet  of  boards  at  $13  per  M ;  167  feet  of  scantling  at  $9.80 
per  M ;  1280  pounds  of  nails  at  20  cents  per  C.     What  was  the 
total  cost? 

141.  To  find  the  cost  of  articles  sold  by  the  ton  of  2000 
pounds. 

1.  What  will  4360  pounds  of  coal  cost  at  $7.50  per  ton? 

SOLUTION 

$7.50  =  cost  of  1  ton  or  2000  Ib. 
$3.75  =  cost  of  \  ton  or  1000  Ib. 
4360  Ib.  =  4.360  thousand  weight. 
4.36  X  $3.75  =  $16.35. 

To  Find   the    Cost  of  Articles  Sold  by  the  Ton  of  2000  Pounds 

a.  Divide  the  price  of  1  ton  by  2  and  the  quotient  will  be  the 
price  of  1000  pounds. 

b.  Reduce  the  pounds  to  thousands  and  decimals  of  a  thou- 
sand by  pointing  off  three  places. 

c.  Multiply  the  price  per  thousand  by  the  number  of  thou- 
sands and  decimals  of  a  thousand. 

2.  At  $18.50  per  ton  what  will  6342  pounds  of  hay  cost? 

3.  At  $22.50  per  ton  what  will  468  pounds  of  hay  cost? 

4.  At  $3.25  per  ton  what  will  1685  pounds  of  soft  coal  cost? 

5.  At  $7.80  per  ton  what  will  2632  pounds  of  hard  coal  cost? 

6.  At  $49.50  per  ton  what  will  be  the  cost  of  42367  pounds 
of  steel  rails? 


96  NEW   BUSINESS   ARITHMETIC 

7.  At  $28.60  per  ton  what  will  be  the  cost  of  26420  pounds 
of  pig  iron  ? 

8.  At  $5.80  per  ton  what  will  be  the  cost  of  a  cargo  consist- 
ing of  48625  pounds  of  salt? 

9.  Bought  48  sacks  of  land  plaster,  each  sack  weighing  180 
pounds  at  $23  per  ton.    What  was  the  cost? 

10.  What  will  be  the  freight  at  $6.25  per  ton  on  five  invoices 
of  merchandise  weighing  as  follows :  2436  pounds,  1972  pounds, 
4837  pounds,  4265  pounds  and  3428  pounds? 


BILLS 

142.  A  Bill  is  a  detailed  account  of  goods  sold  or  services 
rendered,  giving  the  price  of  each  article  and  the  cost  of  the 
whole. 

The  bill  is  said  to  be  "receipted"  when  the  words  "Received 
Payment"  or  "Paid"  are  written  near  the  bottom  with  the  sig- 
nature of  the  seller.  The  bill  is  then  a  receipt  for  the  amount 
paid. 

143.  An  Invoice  differs  in  no  respect  from  a  bill.    The  term 
is  usually  applied  to  goods  bought  in  large  quantities. 

144.  A  Statement  is  an  account  of  bills  rendered,  usually 
during  the  previous  month,  and  give  the  date  of  each  bill  with 
its  total  amount. 

145.  Find  the  cost  of  the  several    articles    and    the    total 
amount  of  each  of  the  following  bills : 

In  billing  it  is  customary  to  count  Ic  extra  where  the  com- 
putation produces  5  mills  or  more,  when  less  than  5  mills  the 
mills  are  dropped.  The  result  is  shown  in  dollars  and  cents. 

Find  the  total  cost  of : 
1.  412  yds.  at  25c.       2.  34  yds.  at  lOc.         3.  25  Ibs.  at  6Jc. 

360  yds.  at  20c.  64  yds.  at  5c.  36  Ibs.  at  12Jc. 

420  yds.  at  12£c.  75  yds.  at  2Jc.  60  Ibs.  at  18Jc. 

350  yds.  at  50c.  46  yds.  at  12Jc.  56  Ibs.  at  25c. 

324  yds.  at  lie.  40  yds  at  GJc.  72  Ibs.  at  31Jc. 

4.  36^  yds.  at  20c.       5.  125  yds.  at  31£c.     6.  72  Ibs.  at  12c. 

75  yds.  at  12Jc.  324  yds.  at  62Jc.          84  Ibs.  at  14c. 

84  yds.  at  6Jc.  136  yds.  at  87Jc.          96  Ibs.  at  16c. 

36  yds.  at  25c.  260  yds.  at  56£c.          87  Ibs.  at  22c. 

90  yds.  at  Sljc.  320  yds.  at  $1.25.         92  Ibs.  at  lie. 

7.  25  pieces  of  gingham :  361,  37,  332,  34,  362,  381,  34,  393, 
422,  41,  40,  411,  42,  411,  43,  462,  421,  393,  38,  362,  37,  393:  41,  421, 
43  at  12jc  per  yard. 

7  97 


98  NEW    BUSINESS   ARITHMETIC 

(*). 

NEW  YORK,  August  15,  1905. 
MR.  WILLIAM  SAMPSON, 

Bought  of  DAVIS  &  JOHNSTON. 

4  Ibs.  Tea @  .50  $*.** 

5  "     Butter @  .32  *.** 

9     "     Bacon @  .12J  *.** 

10     "     Lard @  .09  .** 

4     "     Raisins. @  .22  .** 

3  doz.  Eggs @  .18  .** 

$*.** 
Received  Payment, 

DAVIS  &  JOHNSTON. 

CHICAGO,  January  7,  1905. 
MESSRS.  B.  M.  SMITH  &  Co., 

Bought  of  FINLAY  &  HOLMES. 

8  yds.  Silk @  $1.12J 

15     "      Muslin @       .15 

25     "      Linen @       .08J 

12     "      Calico @       .18 

6     "      Gingham @       .42      

$**.** 
Received  Payment, 

FINLAY  &  HOLMES. 

(10) 

SAN  FRANCISCO,  March  14,  1905. 
WM.  DUNCAN, 

Bought  of  MALZEN  BROS. 

8  prs.  Men's  Thick  Boots @  $3.25 

6     '      Kip  Plow  Shoes @     2.87 J 

4     '      Boys'  Calf  Boots @     1.75 

11     '      Cloth  Gaiters @     2.35 

6     '      Ladies'  Slippers @     1.60 

4     '      Rubbers..  .  @ 


** 


Received  payment  by  note  60  days, 

MALZEN  BROS. 


BILLS  99 

(ii) 

NEW  ORLEANS,  May  15,  1905. 
MESSRS.  DANIEL  C.  HARTWELL  &  Co., 

Bought  of  A.  CARTER  &  Co. 

1640  ft.  A  Flooring @  $24          per  M. 

920    "    C  Flooring @     18 

2467    "    Fencing @     16 

5428    "    Scantling @     13 

1432    "    Timber @       9.37£ 

860    "    Timber @       8.62J 

$**.** 
Received  payment, 

A.  CARTER  &  Co. 

Per  DAVIS. 


(12) 

CLEVELAND,  OHIO,  June  10,  1905. 
MR.  J.  A.  LYONS, 

Bought  of  COLLINS,  HOLBROOK  &  Co. 


15           Granulated  Sugar  , 

@ 

05J 

7     "    Y.  H.  Tea  

@ 

48 

30^  gal.  Molasses  

70 

18  Ibs.  Prunes 

@ 

06J 

3  boxes  Raisins  

..,@ 

1  65 

25  Ibs.  Spice  

..(a) 

10  "     White  Glue  

.  ,\w, 
@ 

40 

$**.** 

Received  Payment, 
COLLINS,  HOLBROOK  &  Co. 


100 


NEW   BUSINESS   ARITHMETIC 


(IS) 

CHICAGO,  ILL.,  June  10,  1903. 
MR.  J.  P.  SHOW, 

Bought  of  HOMER  K.  GOLPIN. 
5  bbls.  A.  C.  Sugar 

316         320        324         330         328 

26          24  29  32  30  @  $5.50 

5  bbls.  Granulated  Sugar 

312         316         310         314         311 

24  20  21  23  20  @  $5.75 

4  bbls.  Loaf  Sugar 

275         284         290         287 
18  20  22  21  @  $5.80 

(U) 

MILWAUKEE,  Wis.,  June  11,  1903. 
MESSRS.  D.  C.  MEYER  &  Co., 

Bought  of  JONES  &  LAUGHLIN. 
20  pc.  Gingham 

341,  33,    322,  361,  371,  382,  313,  321,  34,    351, 
36,    341,  293,  433,  44,    411,  403,  46,    322,  391  @  18j 

18  pc.  do. 

411,  422,  403,  43,    411,  38,    363,  392,  371, 
401,  412,  38,    413,  472,  391,  42,    432,  41     @  16j 

(15) 
PAY   ROLL  PROBLEM 


Names 

Hon. 

Tuea. 

Wed. 

Thurs. 

Pri. 

Sat. 

Ho.  of 
hours 

Per 

hour 

Due 

R  G   Anderson  

8 

9 
8 
8 
7 
7 
10 
8 
6 
5 
8 
10 

8 

9 
8 
8 
7 
6 
10 
8 
6 
4 
9 
10 

9 

8 
8 
9 
8 
6 
8 
S 
8 
4 
8 
10 

9 

8 
8 
10 
8 
Dis 
7 
S 
9 
4 
8 
9 

9 
8 
8 
10 
10 
char 
6 
8 
6 
4 
6 
8 

5 

5 
5 
5 
5 
ged. 
4 
4 
3 
3 
5 
5 

.45 
.40 
.47* 
.25 
.27* 
.30 
.32* 
.37* 
.40 
.50 
52* 
.47* 

G  W  Bridges  

G  J   Buechele  

B   Bullwinkle 

H  R  Bonnes 

L  Berkson 

B  L.  Blose 

A  L  Beck 

A  L  CounzelmEn             

W  F  Carpenter  .           

C  M  Deshlie  .           

R  E  Fisher              

BILLS 


101 


Half  pay  when  out  sick  or  disabled, 
necessary  to  pay  off  help. 


Find  amount  of  money 


(16) 
PAY    ROLL  PROBLEM 


Names 

Hon. 

lues 

Wed. 

Thurs. 

Fri. 

Sat 

No 
ho 

of 
irs 

Day's 
pay 

Pay 

due 

Fahlsing,  O.  F  

10 

10 

10 

10 

10 

10 

fi 

o 

3       ] 

8 

Gearghty,  J.  R  

~q 

q 

10 

10 

10 

10 

3 

Goodfellow  Jos 

8 

8 

"  9 

9 

9 

9 

4 

Gregoldt,  G  J    . 

7 

8 

Q 

5 

10 

10 

4 

Grey,  G.  O  .  .'.  .    . 

5 

5 

5 

5 

5 

5 

5 

Hunt,  J.  C  

5 

4 

4 

5 

Q 

g 

3 

Joyce,  M.  J  

8 

8 

8 

8 

8 

8 

2 

Koellner,  C.  A  

7 

7 

6 

8 

9 

q 

2 

LaRue,  F.  L  

10 

10 

10 

8 

8 

9 

3  50 

Moore,  J.  P  

q 

8 

7 

5 

o 

o 

2  50 

Miller,  H.  W  

8 

0 

() 

5 

10 

10 

4  50 

Perring,  W.  A  

q 

q 

q 

10 

10 

10 

3  25 

|0.*U 

In  the  above  pay  roll  report  10  hours  is  to  count  a  day.  To 
avoid  fractions  in  computation,  multiply  the  number  of  hours  by 
the  pay  and  divide  by  the  number  of  hours  counted  as  a  day's 
work.  When  full  time  has  been  made  multiply  the  number  of 
days  by  the  daily  pay.  Find  amount  of  money  necessary  to  pay 
off  help. 

REVIEW   PROBLEMS 

146.  1.  A  merchant  owes  to  one  man  $146.25,  to  another 
$38.62J,  to  another  $367.80,  to  another  $16.40,  and  to  another 
$54.30.  What  amount  does  he  owe? 

2.  What  will  be  the  cost  of  56  barrels  of  flour  at  $7.25  per 
barrel  ? 

S.  If  16.15  tons  of  railroad  iron  cost  $730.78},  what  will  one 
ton  cost? 

4.  I  owe  A  $267.35,  B  $145.39,  and  C  as  much  as  A  and  B 
and  $16  more.    How  much  do  I  owe  to  all  ? 

5.  Jones  collected  $1624,  and   Davis  collected   .65   of  that 
amount.     How  much  did  they  both  collect? 

6.  A  clerk  earns  $50  a  month.     He  spends  $23.50  for  his 


102  NEW   BUSINESS   ARITHMETIC 

board  and  $8.15  for  other  expenses.    How  much  will  he  save  in 
one  year? 

7.  A  farmer  sold  132.51  bushels  of  corn  for  $44.17.     How 
much  did  he  receive  per  bushel  ? 

8.  A  lady  went  shopping  with  $50.     She  bought  a  cloak  for 
$32,  3  yards  of  silk  at  $2.12J  a  yard,  5  yards  of  cambric  at  $.15  a 
yard  and  3  dozen  buttons  at  $.18.    How  much  money  had  she  re- 
maining ? 

9.  Bought  a  horse  for  $165,  a  yoke  of  oxen  for  $95,  4  cows 
at  $32  each,  and  sold  them  all  for  $400.     How  much  did  I  gain 
or  lose  by  the  transaction? 

10.  A  man  bought  4J  tons  of  hay  for  $48.30J.     How  much 
was  that  per  ton? 

11.  I  owe  A  $185.47;  B  $346.87;  C  $287.36;  D  $418.25;  E 
$29.50;  and  F  $125.75.     I  own  property  worth  $1265.40.     How 
much  do  I  owe  more  than  I  am  able  to  pay  ? 

12.  Bought  640  bushels   of  wheat  at   85   cents   per  bushel. 
After  paying  $185.60  what  remained  yet  unpaid? 

IS.  A  laborer  earns  $1.75  a  day  and  spends  $1.62^  a  day. 
How  much  can  he  save  in  one  year  of  313  working  days? 

14-  A  farmer  owed  $800.  He  paid  265  bushels  of  corn  worth 
45  cents  per  bushel  and  400  bushels  of  wheat  worth  87-J  cents  per 
bushel.  How  much  is  still  unpaid? 

15.  A  merchant  deposited  in  bank  at  one  time  $1725 ;  at  an- 
other $867.50;  at  another  $584.30.     He  then  drew  out  $738.40, 
and  again  deposited  $628.42.     How  much  had  he  then  in  the 
bank? 

16.  A  banker's  expenses  are  $8.75  a  day.     How  much  will 
he  save  in  365  days,  his  income  being  $4000  ? 

17.  Bought  486  barrels  of  apples  for  $1579|.     Sold  one-half 
of  them  at  cost  price  and  the  remainder  at  $3.75  per  barrel.    How 
much  d.id  I  receive  for  them  ? 

18.  A  crop  of  wheat  amounting  to  3420  bushels  was  sold  for 
$1881.    How  much  was  that  per  bushel  ? 

19.  Bought  165  barrels  of  apples  of  3  bushels  each  at  35 
cents  per  bushel  and  sold  the  whole  for  $200.    How  much  did  I 
gain? 


BILLS  103 

20.  A  drover  bought  cattle  at  $46.56  per  head,  and  sold  them 
at  $65.42  per  head,  and,  thereby  gained  $3526.82.     How  many 
cattle  did  he  buy  ? 

21.  If  26  men  receive  $988  for  38  days'  work,  how  much  does 
each  man  earn  a  day? 

22.  A  gentleman  dying  left  one-third  of  his  estate  amounting 
to  $48000  to  his  widow  and  the  remainder  to  his  six  children 
equally.     What  was  the  portion  of  each  child? 

23.  If  25  men  perform  a  piece  of  work  for  $2000,  and  spend, 
while  doing  it,  $163.75,  what  will  be  each  man's    share    of   the 
profits  ? 

24.  What  is  the  cost  of  24865  pounds  of  hay  at  $23.50  per  ton? 

25.  A  grocer  bought  a  hogshead  of  molasses  containing  63 
gallons  for  $49.14;   9  gallons  leaked  out  and  he  sold  the  re- 
mainder at  85  cents  per  gallon.    Did  he  gain  or  lose  on  the  en- 
tire quantity,  and  how  much  ? 

26.  If  5f  barrels  of  flour  cost  $28f  what  will  13 j  barrels  cost? 

27.  Wliat  is  the  cost  of  seven  pieces  of  cambric,  each  piece 
containing  23  yards  at  12J  cents  per  yard? 

28.  Reduce  — y  to  a  decimal  fraction. 

29.  What  cost  1827  pounds  of  fertilizer  at  $32.40  per  ton? 

80.  John  runs  45  rods  a  minute  and  William  pursues  him  at 
the  rate  of  50  rods  a  minute.    If  John  has  5  minutes  the  start  of 
William,  how  long  will  it  require  William  to  overtake  John? 

81.  Reduce  .0625  to  a  common  fraction. 

32.  What  is  the  cost  of  14620  bricks  at  $5.60  per  M  ? 
88.  What  will  T8oVo  of  a  cord  of  wood  cost  at  $5.65  per  cord? 
34.  Reduce   5\,    .62J,   .37TV,   f   to   decimals,   and   find   their 
sum. 

85.  A  miller  bought  356|  bushels  of  wheat  of  one  man  and 
145  of  another  at  62£  cents  per  bushel.    He  sold  f  of  the  entire 
quantity  at  a  profit  of  $52.80,  and  the  balance  at  68£  cents  per 
bushel.     How  much  did  he  gain  or  lose  by  the  transaction? 

86.  Find  the  number  of  gallons  in  5  barrels  of  cider  if  the 
first  contained  31.375  gallons,  the  second  38.0002  gallons,  the 


104  NEW  BUSINESS  ARITHMETIC 

third  34.4  gallons,  the  fourth  36.12  gallons,  and  the  fifth  35  gal- 
lons. 

37.  A  man  bequeathed   .125  of  his  property  to  an   orphan 
asylum,  -f$  to  his  son,  and  the  remainder,  which  was  $24120,  to 
his  wife.     What  was  the  value  of  his  property? 

38.  A  dealer's  sales  of  carpeting  and  matting  for  a  year  were 
$264320,  and  the  sales  of  matting  were  .1875  of  the  total  sales. 
The  cost  of  the  carpeting  was  .75  of  its  sales,  and  the  total  ex- 
penses of  the  business  were  .15625  of  the  cost  of  the  carpeting. 
What  were  the  sales  of  the  matting?    Of  the  carpeting?    What 
was  the  cost  of  the  carpeting  ?    What  were  the  total  expenses  ? 


REDUCTION  OF  DENOMINATE  NUMBERS 

147.  Reduction  is  the  process  of  changing  a  number  from 
one  denomination  to  another  without  altering  its  value. 

148.  Reduction  Descending  is  changing  a  number  from  a 
higher  to  a  lower  denomination.     Thus,  1  foot  changed  to  12 
inches. 

149.  Reduction  Ascending  is  changing-  a  number  from  a 
lower  to  a  higher  denomination.    Thus,  16  ounces  changed  to  1 
pound. 

VALUE 

150.  1.    United  States  Money 

TABLE 

10  mills  (m.)  make  1  cent ct. 

10  cents  1  dime d. 

10  dimes  1  dollar $ 

10  dollars  1  eagle E. 

151.  A  Legal  Tender  is  money  which,  if  offered,  legally  will 
save  the  debtor  from  further  interest  and  from  costs  of  suit. 

NOTES. — 1.  All  the  gold  coins,  and  the  silver  coins  of  $1  and  upwards, 
except  the  trade  dollar,  are  legal  tender  for  all  payments. 

2.  Silver  coins  less  than  $1  are  legal  tender  to  the  amount  of  $10; 
nickel  and  bronze  pieces  to  the  amount  of  25  cents. 

II.    Canada  Money 

152.  Canada  Money  is  the  legal  currency  of  the  Dominion 
of  Canada.     It  is  founded  on  the  Decimal  Notation,  and  its  de- 
nominations, Dollars,  Cents  and  Mills,  have  the  same  nominal 
value  as  the  corresponding  denominations  of  United  States  money. 
Hence,  all  the  operations  in  it  are  the  same  as  those  in  United 
States  money. 

105 


106  NEW   BUSINESS   ARITHMETIC 

III.     English  Money 
153.  English  Money  is  the  currency  of  Great  Britain. 


TABLE 
4  farthings  (far.)  make  1  penny  .......  d. 

12  pence  1  shilling  ......  s. 

20  shillings      .  1  pound  or  sov.  .  £ 


NOTES.  —  1.     The  gold  coins  are  the  sovereign   (=  £1),  and  the  half- 
sovereign. 

2.  The  silver  coins  are  the  crown  (=  5s.),  the  half-crown  (=  2s.  6d.), 
the  florin,  the   shilling,   and   the   six-penny,   four-penny  and  three-penny 
pieces. 

3.  The  copper  coins  are  the  penny,  halfpenny  and  farthing. 

4.  The  guinea  (=  21s.)  and  the  half-guinea  (=  10s.  6d.  sterling),  are 
old  gold  coins,  and  are  no  longer  coined. 

Money  Equivalents 

1  pound  English  $4.8665 

1  shilling                               do  .24j 

1  crown  Austria  .203 

1  mark  Germany  .238 

1  franc  France  .193 

1  lira  Italy  .193 

1  ruble  Russia  .772 

154.  To  perform  reduction  descending. 
1.  Reduce  £3  8s.  lOd.  3  far.  to  farthings. 

SOLUTION 

£3  8s.  lOd.  3  far. 
20 

68s. 
12 


826d. 


3307  far. 


REDUCTION   OF   DENOMINATE   NUMBERS  107 

From  the  foregoing  we  have  the  following  rule  for 
Reduction  Descending 

a.  Multiply  the  highest  denomination  by  that  number  which 
will  reduce  it  to  the  next  lower  and  add  the  given  number  of  that 
denomination,  if  any. 

b.  Proceed  in  the  same  manner  with  the  results  obtained  in 
each  denomination  until  th}>  zvholc  is  reduced. 

155.  To  perform  reduction  ascending. 

2.  Reduce  3307  farthings  to  pounds. 

SOLUTION 

4)3307  far. 
12)   826d.  +  3  far. 
20) 68s  +  lOd. 

£3  +  8s. 

£3  8s.  lOd.  3  far. 

From  the  foregoing  we  have  the  following  rule  for 
Reduction  Ascending 

a.  Divide  the  given  number  by  that  number  which  will  reduce 
it  to  the  next  higher  denomination. 

b.  Divide  the  quotient  by  the  next  higher  number  in  the  same 
manner;  and  so  proceed  to  the  highest  denomination  required* 
The  last  quotient,  with  the  several  remainders  will  be  the  answer. 

NOTE. — Reduction  descending  and  reduction  ascending  mutually  prove 
each  other. 

3.  Reduce  £-23  9s.  8d.  3  far.  to  farthings. 

4.  Reduce  7868d.  to  higher  denominations. 

5.  Reduce  £10  9s.  6d.  2  far.  to  farthings. 

6.  Reduce  5s.  3d.  1  far.  to  farthings. 

7.  In  17852  far.  how  many  pounds? 

8.  In  £83  6s.  3  far.  how  many  farthings? 
0.  In  1624d.  how  many  pounds? 

10.  In  £1428  how  many  pence? 


108  NEW   BUSINESS   ARITHMETIC 

WEIGHT 

156.  W eight  is  the  measure  of  the  force  of  gravity  which 
draws  all  bodies  towards  the  center  of  the  earth. 

The  standard  of  weight  in  the  United  States  is  the  troy  pound. 

157.  There  are  three  kinds  of  weights  used  in  the  United 
States,  viz. :  Avoirdupois,  Troy  and  Apothecaries. 

I.    Avoirdupois  Weight 

158.  Avoirdupois  or  Commercial  Weight  is  used  for  weigh- 
ing ordinary  articles,  such  as  groceries,   farm  produce  and  all 
metals  except  the  precious  metals. 

TABLE 

16  drams    (dr.)    make  1  ounce    oz. 

16  ounces  1  pound    Ib. 

100  pounds  "      1  hundred-weight,    cwt 

20  cwt.,or20001bs.    "      1  ton   T. 

112  Ibs.  =  1  long  hundred  -  weight. 

2240  Ibs.  =  1  long  ton. 

NOTES. — 1.  In  the  United  States  Custom  House  and  in  wholesale 
transactions  in  coal  and  iron,  the  long  ton  is  used. 

2.  The  avoirdupois  pound  is  determined  from  the  standard  troy 
pound,  and  contains  7000  troy  grains. 

Special  Avoirdupois  Weights 

100  pounds  of  Dry  Fish  make  1  Quintal. 

100  Nails  1  Keg. 

196  Flour  "  1  Barrel. 

200  Pork  or  Beef  "  1  Barrel. 

280  Salt  at  N.  Y.  S.  Works     "  1  Barrel. 

240  Lime  "  1  Cask. 

159.  Gross    Weight   is   the   weight   of   the  goods   together 
with  the  box,  cask  or  whatever  contains  them. 

160.  Net  Weight  is  the  weight  of  the  goods  alone. 
Tare  is  the  allowance  made  for  the  weight  of  the  packing. 
When  grain  and  seeds  are  bought  and  sold  by  weight  so  many 

pounds  are  considered  as  a  bushel.    The  following  table  gives  the 
weights  in  general  use: 


REDUCTION   OF   DENOMINATE   NUMBERS 


109 


TABLE  OF  POUNDS  PER  BUSHEL 


Commodities 

Lbs. 

Commodities 

Lbs. 

Commodities 

Lbs. 

Barley 

48 

Corn   Shelled. 

56 

Potatoes 

60 

Beans      .    .    . 

60 

Corn  in  Ear 

70 

Rve 

56 

Buckwheat  

48 

Flax  Seed 

56 

Timothy  Seed 

45 

Blue  Grass  Seed.  . 

14 

Malt 

34 

Wheat          

60 

Coal,  Bituminous. 

80 

Oats  

32 

Wheat  Bran  

20 

NOTE. — See  page  352  for  weights  of  other  articles. 

1.  Reduce  3  cwt.  2  Ibs.  to  pounds. 

2.  Reduce  2  T.  5  cwt.  to  pounds. 

3.  Reduce  5  cwt.  15  Ibs.  13  oz.  to  ounces. 

4.  Reduce  2  cwt.  14  Ibs.  3  dr.  to  drams. 

5.  Reduce  3  T.  7  cwt.  18  Ibs.  11  oz.  14  dr.  to  drams. 

6.  In  4307  Ibs.  how  many  cwt? 

7.  In  12600  Ibs.  how  many  tons? 

8.  In  2048000  dr.  how  many  tons? 

9.  In  64546  dr.  how  many  cwt.? 

10.  Reduce  544272  dr.  to  T. 

11.  A  merchant  bought  4  T.  8  cwt.  42  Ibs.  of  castings  at  12c 
per  pound.    What  did  the  whole  cost  him  ? 

12.  A  coal  dealer  bought  176960  Ibs.  of  hard  coal  at  $5.25 
per  long  ton  and  sold  it  at  $5.75  per  short  ton.    What  did  he  gain? 

13.  A  grocer  bought  3  hogsheads  of  sugar :    The  first  weigh- 
ing 8  cwt.  13  Ibs.  at  4Jc  per  pound;  the  second  weighing  7  cwt. 
82  Ibs.  at  4fc  per  pound;  the  third  weighing  9  cwt.  43  Ibs.  at 
4|c  per  pound.     He  sold  the  whole  by  retail  at  5c  per  pound. 
What  was  his  net  profit? 

14-  Bought  5  barrels  of  pork  at  7|c  per  pound  and  sold  it  at 
9c  per  pound.     What  was  my  gain? 

15.  What  is  the  weight  of  250  barrels  of  flour? 

16.  A  grocer  bought  3  barrels  of  salt  at  $1.25  per  barrel,  and 
retailed  it  at  f  of  a  cent  per  pound.    What  did  he  gain? 

17.  At  45c  per  bushel  what  will  be  the  value  of  4865  Ibs.  of 
shelled  corn? 

18.  A  farmer  sold  8750  Ibs.  of  oats  at  18c  per  bushel.    What 
did  they  bring? 

19.  Find  the  value  of  4627  Ibs.  flax  seed  at  $3.60  per  bushel. 

20.  What  cost  5180  pounds  timothy  seed  at  $1.45  per  bushel? 


110  NEW   BUSINESS   ARITHMETIC 

II.    Troy  Weight 

161.  Troy  Weight  is  used  in  weighing  gold,  silver  and  other 
precious  metals. 

TABLE 

24  grains  (gr.)  make  1  pennyweight. .  .pwt. 

20  pennyweights  "      1  ounce oz. 

12  ounces  1  pound Ib. 

In  addition  to  the  above,  the  following,  called  Diamond  Weight, 
is  used  in  weighing  diamonds  and  other  precious  stones: 

TABLE 

16  parts  make  1  carat  grain  =    .792  troy  grains. 

4  carat  grains  "     1  carat  =  3.168     " 

NOTE. — The  term  carat  is  also  used  to  denote  the  fineness  of  gold,, 
and  means  ^  part.  Thus,  gold  18  carats  fine  contains  18  parts  pure  gold 
and  6  parts  alloy. 

1.  Reduce  4  Ibs.  to  grains. 

2.  Reduce  3  Ibs.  5  oz.  15  pwt.  to  pwt. 

3.  Reduce  13  Ibs.  9  oz.  16  pwt.  22  gr.  to  grains, 

4.  Reduce  146  gr.  to  pwt. 

5.  Reduce  32625  gr.  to  pounds. 

6.  A  jeweler  sold  a  gold  chain  weighing  2  oz.  16  pwt.  11  gr. 
at  4c  per  grain.    How  much  did  he  receive  ? 

7.  A  miner  dug  17  Ib.  8  oz.  9  pwt.  of  gold  and    sold   it   at 
60c  per  pwt.    What  did  it  bring? 

8.  A  goldsmith  manufactured  1  Ib.  1  pwt.  16  grs.  of  gold 
into  rings,  each  weighing  4  pwt.  20  gr.     He  sold  the  rings  for 
$1.25  apiece;  what  did  he  receive  for  them? 

9.  Eight  watch  cases  each  14  carats  fine   and  weighing   60 
pwt.  contain  how  many  ounces  of  gold? 

10.  What  is  the  value  of  a  diamond  weighing  T36  of  a  carat 
at  $75  per  carat? 


REDUCTION   OF   DENOMINATE   NUMBERS 


111 


III.    Apothecaries'  Weight 

162.  Apothecaries'  Weight  is  used  by  druggists  in  com- 
pounding medicines. 

Druggists  purchase  their  medicines  at  wholesale  by  avoirdu- 
pois weight. 


I  M 


TABLE 


20  grains   (gr.  xx)   makel  scruple ...  sc.  or   3. 

3  scruples   (3iij)      "     1  dram dr.    or   3. 

8  drams   (3  viij)       "     1  ounce oz.  or  3- 


12  ounces    (3  xij) 


1  pound Ib.  or  ft>. 


NOTES. — 1.  The  pound,  ounce  and  grain  of  this  weight  are  the  same  as 
those  of  troy  weight;  the  pound  of  each  contain'  12 ^z.  =  5760  gr. 

2.  In  writing  quantities  in  apothecaries'  weigHt  the  characters  de- 
noting the  denomination  precede  the  quantity  except  in  p6i|nds.  In  prac- 
tice the  quantities  are  usually  written  in  the  Roman  numerals. 

1.  Reduce  5  Ib.  to  grains. 

2.  Reduce  11  Ib.  33  to  3.  f 

3.  Reduce  2  Ib.  B2  32  32  gr.2  to  grains. 

4.  In  §48  how  many  pounds? 

5.  Reduce  gr.3864  to  ounces. 

6.  In  gr.25941  of  rhubarb  how  many  pounds? 

7.  A  druggist  put  up  gr.263?6  of  medicine  into  prescrip- 
tions, each  prescription  contained   92  gr.16.     How  many  pre- 
scriptions did  he  make? 

8.  How  much  medicine  will  a  druggist  put  up  in  one   year 
of  365  days  if  he  averages  8  prescriptions  a  day  of  gr.20  each? 

9.  An  apothecary  bought  3  pounds  of  medicine   (apotheca- 
ries' weight)  at  $6  per  pound  and  retailed  it  at  10  cents  per  3. 
What  was  his  total  gain  ? 

10.  What  is  gained  by  buying  4  Ibs.  of  quinine  (apothecaries' 
weight)  at  $5.50  per  Ib.  and  after  manufacturing  it  into  capsules 
of  gr.2  each,  selling  them  at  25c  per  dozen? 

11.  A  case  of  drugs  weighs  14  Ibs.  37  34.     What  is  it  worth 
at  5c  per  grain  ? 


112  NEW   BUSINESS   ARITHMETIC 

Comparison  of  Weights 

163.  The   Standard    Unit   in   both   troy    and    apothecaries 
weights  is  the  troy  pound  containing  5760  troy  grains. 

164.  The  Standard  Unit  in  avoirdupois  weight  is  the  pound 
which  is  equal  to  7000  troy  grains. 

COMPARATIVE   TABLE    OF    WEIGHTS 

Troy  Apothecaries  Avoirdupois 

1  pound  =  5760  grains  =  5760   grains  =  7000  grains 
1  ounce  =    480       "       =    480       "        =  437.5     " 

175  pounds  =    175   pounds  =  144  pounds 

1.  Change  25  Ib.  7  oz.  15  pwt.  troy  to  avoirdupois  pounds. 

2.  A  druggist  bought  at  wholesale  15  Ib.  quinine  at  $5.50  per 
pound  avoirdupois,  and   after   making  the  entire  quantity  up 
into  2  gr.  pills  sold  the  pills  at  40c  per  dozen.   What  did  he  gain  ? 

3.  A  case  of  drugs  weighs  76  Ibs.  avoirdupois.     How  much 
is  that  troy  ? 

4.  In  65  Ibs.  avoirdupois,  how  many  troy  pounds? 

5.  Bought  16  Ib.  of  opium,  avoirdupois  weight,  at  50c  an 
ounce  and  sold  the  same  by  apothecaries'  weight  at  60c  an  ounce. 
What  was  my  gain  ? 

6.  In  243  oz.  troy  how  many  ounces  avoirdupois  ? 

7.  What  is  gained  by  buying  8  Ib.  of  quinine  at  $6  per  Ib. 
avoirdupois  weight,  and  selling  same  at  Jc  per  grain  apothecaries' 
weight  ? 

8.  Reduce  75  oz.  apothecaries'  weight  to  ounces  avoirdupois 
weight. 

9.  Reduce  36  Ib.  avoirdupois  weight  to  pounds  troy  weight. 

10.  What  is  gained  by  buying  25  Ib.  avoirdupois  weight  at 
$3  per  Ib.,  and  selling  at  $3.20  apothecaries'  weight? 

11.  Change   10  Ib.   9  oz.  avoirdupois  weight  to  Ib.   and  oz. 
troy  weight. 

12.  Change  31  Ib.  11  oz.  apothecaries'  weight  to  Ib.  and  oz. 
avoirdupois  weight. 

IS.  Is  a  pound  of  feathers  heavier  than  a  pound  of  gold,  and 
how  much  ? 


REDUCTION   OF   DENOMINATE   NUMBERS 


113 


MEASURES 

165.  A  Measure  is  a  standard  unit  established  by  law  or  cus- 
tom, by  which  the  length,  surface,  capacity  and  weight  of  things 
are  estimated. 

Measures  are  of  two  kinds :  Measures  of  Extension  and  Meas- 
ures of  Capacity. 

166.  Extension  is  that  property  of  matter  which  causes  it  to 
occupy  space.    It  may  have  one  or  more  of  the  three  dimensions : 
Length,  breadth  and  thickness. 

A  Line  has  only  one  dimension — length. 

A  Surface  has  two  dimensions — length  and  breadth. 

A  Solid  has  three  dimensions — length,  breadth  and  thickness. 

MEASURES  OF  EXTENSION 

167.  Measures  of  Extension  embrace  Long  or  Linear  Meas- 
ure, Square  Measure  and  Cubic  Measure. 

I.    Long  Measure 

168.  Long  Measure,  also  called  Linear  Measure,  is  used  in 
measuring  distances  or  length. 


12 
3 
5 

40 

320 

5280 

3 


inches  (in.) 

feet 

yds.  or  16  }  ft. 

rods 

rods,  or  ) 

feet,         i 

geog.  miles 


—  1  league 1. 

NOTES. — 1.  The  yard  for  common  use  is  divided  into  halves,  quarters, 
eighths  and  sixteenths.  At  the  United  States  Custom  Houses  it  is  divided 
into  tenths  and  hundredths. 

2.  The  mile  of  5280  feet  is  the  legal  mile  in  the  United  States  and 
England  and  is  called  the  statute  mile. 

3.  The  inch  may  be  divided  into  halves,  fourths,  eighths,  etc.,  or  into 
tenths,  hundredths,  etc. 


114  NEW   BUSINESS   ARITHMETIC 

Special  Linear  Measures 

Ys  inch  =  1  size.     Used  by  shoemakers. 

4  inches  =  1  hand.    Used  in  measuring  the  height  of  horses. 

6  feet  =  1  fathom.     Used  in  measuring  depths  at  sea. 

1.152%  statute  mi.  =  1  geographic  mile.   Used  in  measuring  distances  at  sea. 

3  geog.  mi.  -  1  league.    Used  in  measuring  distances  at  sea. 

1  knot  =  1  geog.  mi.    Used  in  measuring  speed  of  vessels.* 

60  geog.  mi.  { j    1  degree  of  long,  on  the  equator,  or 

69.16  statute  mi.  (      ]    1  degree  of  a  meridian. 

360  degrees  =  circumference  of  the  earth. 

NOTE. — *The  progress  of  sailing  vessels  is  determined  by  a  half -min- 
ute glass  and  a  log  line,  which  is  divided  into  knots,  bearing  the  same  ratio 
to  a  mile  that  a  half-minute  has  to  an  hour. 

1.  Reduce  2  yds.  2  ft.  7  inches  to  inches. 

2.  Reduce  7  yards  8  inches  to  inches. 

3.  Reduce  5  mi.  to  rods. 

4-  Reduce  8  mi.  225  rods  to  rods. 

5.  Reduce  16  mi.  25  rds.  to  rods. 

6.  Reduce  18  rds.  2  yds.  1  ft.  9  in.  to  inches. 

7.  Reduce  12760  in.  to  higher  denominations. 

8.  Reduce  78980  ft.  to  higher  denominations. 

9.  Find  the  cost  of  building  a  fence  1  mi.  165  rds.  4  yds.  long 
at  18|c  per  yard. 

10.  A  lake  is  30  fathoms  5  ft.  10  in.  deep.    How  many  inches 
deep  is  it? 

11.  If  a  vessel  travels  15  knots  an  hour,  how  many  league? 
will  she  travel  in  2  days  of  24  hrs.  each  ? 

12.  What  will  it  cost  to  fence  a  square  field  at  2Jc    per  ft., 
the  sides  of  which  are  14  rd.  2  yd.  1  ft.  ? 

13.  I  built  four  fences  at  30c  per  yd.    The  first  was  112  rd. 
1£  yd.  long;  the  second  23  rd.  1  ft.  long;  the  third  1  fur.  16  rd. 

4  yd.  2  ft.  long;  the  fourth  32  rd.  long.    What  was  the  cost? 

14.  How  many  inches  high  is  a  horse  which  measures  16£ 
hands  ? 

15.  A  vessel  travels  at  the  rate  of  20  knots  an  hour.     How 
many  statute  miles  will  she  go  in  96  hours? 

16.  The  drive  wheels  of  a  locomotive  are  24  ft.  6  in.  in  cir- 
cumference.    How  many  times  will  they  revolve  in  going  a  dis^ 
tance  of  40  mi.  118  rd.  1  yd.? 


REDUCTION   OF   DENOMINATE   NUMBERS 


115 


Surveyors'  Long  Measure 

169.  Surveyors'  Long  Measure  is  used  by  surveyors  and 
engineers  in  measuring  the  dimensions  of  land,  distance,  etc. 

The  Linear  Unit  commonly  employed  by  surveyors  is  a  Gun- 
ter's  Chain,  which  is  4  rods  or  66  feet  long,  and  divided  into  100 
links. 


TABLE 

7.92  inches  (in.)       make  1  link 1. 

25  links  1  rod  or  pole..r. 

4  rods  or  100  links  "      1  chain  ....  ch. 

80  chains  "      1  mile  .      .  .mi. 


NOTE.— In  measuring  roads,  etc.,  engineers  use  a  chain,  or  measuring 
tape,  100  feet  long,  each  foot  being  divided  into  tenths  and  hundredth*. 

1.  Reduce  22  ch.  44  1.  to  inches. 

2.  Reduce  2  mi.  70  ch.  10  1.  to  inches. 

3.  Reduce  1  mi.  20  ch.  to  feet. 

4.  Reduce  4  mi.  36  ch.  to  yards. 

5.  Reduce  16384  1.  to  mi. 

6.  A  farm  is  45  ch.  16  1.  long  and  32  ch.  18  1.  wide, 
many  feet  of  fence  will  be  required  to  enclose  it? 


How 


II.     Square  Measure 

170.  Square  or  Surface  Measure  is  used 
in  measuring  surfaces;  as  land,  board,  amount 
of  painting,  plastering,  papering,  paving,  etc. 

171.  A   Rectangle  is  a   flat  surface  with 
four  square  corners. 

172.  A  Square  is  a  rectangle  whose  four 
sides  are  equal. 

A  Square  Inch  is  a  square  each  side  of 
which  is  1  inch  in  length.  A  Square  Foot  is 
a  square  each  side  of  which  is  1  foot  in  length. 
A  Square  Yard  is  a  square  each  side  of  which 
is  1  yard  in  length. 


FEET 


A  RECTANGLE. 


FEET 


A  SQUARE. 


116  NEW   BUSINESS   ARITHMETIC 

The  figure  shows  that  1  square  yard,  that  is  3  feet  square,  con- 
tains 9  square  feet,  and  from  this  we  deduce  the  principle,  that 

The  area  or  surface  of  a  square  or  rectangle  may  be  found  by 
multiplying  the  length  by  the  breadth. 

TABLE 

4  square  inches  (sq.  in.)  make  1  square  foot .  . .  .sq.  ft. 
9  square  feet  1  square  yard . . .  sq.  yd. 
0  square  yards  "  1  square  rod sq.  rd. 

square  rods  **      1  acre A. 

acres  1  square  mile... sq.  mi. 

NOTE. — Paving,  painting,  calcimining,  etc.,  are  estimated  by  the  square 
of  100  square  feet. 

1.  Reduc.:  6  sq.  yd.  to  square  inches. 

2.  Reduce  10  A.  to  square  rods. 

3.  Reduce  1  sq.  mi.  to  square  rods. 

4.  Reduce  2  sq.  yd.  5  sq.  ft.  to  square  inches. 

5.  Reduce  5  A.  85  sq.  rd.  20  sq.  yd.  7  sq.  ft.  to  square  feet. 

6.  Reduce  65  A.  115  sq.  rd.  13  sq.  yd.  5  sq.  ft.  120  sq.  in.  to 
square  inches. 

7.  Reduce  960  sq.  rd.  to  acres. 

8.  Reduce  2467  sq.  in.  to  square  yards. 

9.  Reduce  4178  sq.  in.  to  square  yards. 

10.  Reduce  16328  sq.  in.  to  higher  denominations. 

11.  How  many  square  feet  in  a  square  measuring  7  ft.  on  a 
side? 

12.  What  is  the  area  in  acres  of  a  rectangular  field  measuring 
150  rd.  long  by  80  rd.  wide  ? 

13.  How  much  greater  is  tne  area  of  a  lot  25  yd.  square  than 
a  lot  containing  25  sq.  yd.? 

14.  How  many  yards  of  carpeting  1  yd.  wide  will  be  required 
to  carpet  a  room  27  ft.  long  and  18  ft.  wide? 

15.  What  will  it  cost  to  paint  a  blackboard  46  ft.  long  and  4J 
ft.  wide,  at  27c  per  sq.  yd.  ? 

16.  Find  the  cost  of  paving  a  street  600  ft.  long  and  46  ft. 
wide  at  85c  per  square. 


REDUCTION   OF   DENOMINATE   NUMBERS  1 17 

17.  Find  the  cost  of  plowing  a  field  58  rods  long  and  34  rods 
wide  at  $2.20  per  A. 

18.  Find  the  number  of  square  feet  in  the  walls  and  ceiling 
of  a  room  20  ft.  long,  16*ft.  wide  and  9  ft.  6  in.  high. 

19.  What  will  it  cost  at  $3.14  per  square  to  plaster  a  court 
room  48  ft.  long,  36  ft.  wide  and  25  ft.  high? 

20.  What  will  it  cost  at  $4.40  per  square    to    put    the    roof 
on  a  house  52  ft.  long,  the  rafters  being  22  ft.  on  each  side? 

21.  At  $23  per  A.  what  is  the  cost  of  a  field  38  rd.  long  and 
30  rd.  wide? 

22.  Find  the  cost  of  a  farm  80  rd.  long  and  33  rd.  wide,  at 
$36.50  per  A. 

23.  How  many  yd.  of  carpet  J  yd.  wide,  laid  lengthwise,  will 
it  take  to  cover  a  floor  22  ft.  long  and  15  ft.  wide? 

24.  What  will  it  cost  to  carpet  a  room  30  ft.  long  and  25  ft. 
wide,  with  carpet  1J  yd.  wide,  laid  lengthwise,  at  80c  per. yard? 

25.  Find  the  cost  of  carpeting  a  room  36  ft.  long,  28  ft.  wide 
with  carpet  J  yd.  wide,  laid  lengthwise,  at  $1.15  per  yard. 

26.  Find  the  number  of  strips  of  carpet  1J  yd.   wide  run 
lengthwise  of  a  floor  32  ft.  long  and  27  ft.  wide.    What  does  it 
cost  at  $1.10  per  yd.,  allowing  a  waste  of  J  yd.  on  each  strip  for 
matching  ? 

27.  What  will  it  cost  at  60c    per  sq.  yd.  to  concrete  a  walk 
360  ft.  long  and  10  ft.  6  inches  wide? 

28.  What  will  it  cost  at  4c   per  sq.  yd.   to  build  a  walk  14  ft. 
wide  around  a  block  240  ft.  square  ? 

29.  What  will  it  cost  at  12Jc   per  sq.  yd.  to  paper  the  walls 
and  ceiling  of  a  room  20  ft.  long,  16  ft.  wide  and  9  ft.  high? 

50.  What  will  it  cost  to  plaster  the    sides   and    ceiling   of   a 
room  36  ft.  9  in.  long,  27  ft.  6  in.  wide  and  10  ft.  6  in.  high,  at 
21c   per  sq.  yd.,  if  28  sq.  yd.  be  allowed  for  doors  and  windows? 

51.  The  length  of  a  rectangular  fish  pond  is  90  ft,  and    its 
width  75  feet.    Immediately  surrounding  this  pond  is  a  sidewalk 
12  ft.  wide.     What  is  the  distance  around  the  outer  edge  of  the 
sidewalk  ? 

32.  A  contractor  received  $247.50  for  flagging  a  court-yard 
30  feet  long,  at  $2.75  per  square  yard.  What  was  the  width  of 
the  yard  ? 


118  KEW   BUSINESS   ARITHMETIC 

33.  What  is  the  difference  in  the  areas  of  two  rectangles,  one 
15  rd.  long  and  18J  ft.  wide,  and  the  other  71  yd.  long  and  3  rd. 
wide  ? 

34.  A  tinsmith  covered  a  roof  with  "1152  sheets  of  tin,  each 
sheet  covering  40  by  20  inches.  How  many  square  feet  of  roof 
were  there  ? 

Board  Measure 

173.  Board  Measure  is  used  by  lumbermen  in  estimating  the 
contents  of  boards,  plank,  joists,  beams,  etc. 

174.  A  Board  Foot  is  1  ft.  long  1  ft.  wide  and  1  in.  thick, 
or  a  square  foot  1  inch  thick. 

Boards  1  inch  or  less  in  thickness  contain  as  many  board  feet 
as  the  surface  of  the  board  in  square  feet. 

Boards  more  than  an  inch  in  thickness,  and  all  squared  lumber, 
are  estimated  by  the  number  of  square  feet  of  boards  one  inch 
in  thickness  to  which  they  are  equivalent.  Round  timber  such  as 
masts,  poles,  etc.,  are  estimated  by  cubic  feet. 

175.  When  lumber  is  one  inch  or  less  in  thickness,  to    find 
the  number  of  board  feet,  multiply  the  length  in  feet  by  the  width 
in  inches  and  divide  by  12. 

When  more  than  one  inch  in  thickness,  the  above  result  must 
be  multiplied  by  the  number  of  inches  thick. 

How  many  feet,  board  measure,  in  the  following: 

1.  A  board  16  ft.  long,  1  ft.  wide  and  J  in.  thick? 

2.  A  board  24  ft.  long,  9  in.  wide  and  1  in.  thick  ? 

3.  A  board  14  ft.  long,  1|  ft.  wide  and  2  in.  thick? 

4.  25  boards  12  ft.  long,  8  in.  wide  and  1 J  in.  thick  ? 

5.  A  stick  of  timber  6-  in.  by  8  in.  and  18  ft.  long? 
£.16  joists  2  in.  by  4  in.   and  13  ft.  long? 

7.  40  2-inch  planks  14  in.  wide  and  14  ft.  long? 

8.  36  3-inch  planks  9  in.  wide  and  20  ft.  long? 

9.  A  stick  1  ft.  by  1J  ft.  and  27  ft.  long? 

10.  What  will  it  cost  at  $1.60  per  hundred,  to  build  a  side- 
walk 40  yd.  long,  6  ft.  wide,  with  planks  f  in.  thick? 


REDUCTION   OF   DENOMINATE   NUMBERS 


119 


11.  What  will  it  cost  at  $18  per  thousand  for  lumber  1^  in. 
thick,  to  lay  a  floor  in  a  room  19  by  24  ft.,  J  being  allowed  for 
matching  the  lumber  ? 

12.  At  $12.50  per  thousand,  what  will  the  lumber  cost    for 
siding  a  house  30  ft.  long,  24  ft.  wide  and  16  ft.  high,  30  sq.  yd. 
being  allowed  for  doors  and  windows  and  the  gable  ends  being 
counted  544  sq.  ft.  ? 

13.  Find  the  cost  of  the  following  bill  of  lumber:    10  pc.  2x4- 
14;  12  pc.  2x6-16;  20  pc.  2x8-18;  24  pc.  4x4-20;  20  pc.  4x8-20 
@  $21  per  M. ;  96  pc.  2x12-16 ;  75  pc.  2x10-18  @  $25  per  M. 

Surveyor's  Square  Measure 

176.  Surveyors  Square  Measure  is  used  in  computing  the 
area  or  contents  of  land. 

177.  A  Principal  Meridian  is  a  true  north  and  south  line 
established  as  a  basis  for  government  surveys.    There  are  in  the 
United  States  twenty-four  principal  meridians. 

The  meridians  estab- 
lished for  the  purpose  of 
government  survey  must 
not  be  confounded  with 
meridians  of  longitude 
used  by  astronomers  and 
navigators,  as  they  are 
entirely  different.  The 
principal  meridians  used 
in  surveying  land  are 
usually  located  with  ref- 
erence to  some  natural 
landmark,  such  as  the 
mouth  of  a  river,  and 
are  not  equi-distant 
apart. 

The  first  principal 
meridian  starts  from  the 
junction  of  the  Miami 
and  Ohio  rivers,  form- 
ing the  boundary  be- 
tween Indiana  and  Ohio; 
the  second  starts  from  a 
point  two  and  a  half 
miles  west  of  the  junc- 
tion of  the  Little  Blue 


CO 

RRECTIC 

1 
N 

T 

6 

i 

T.6N. 
R.4E. 

T.5  N. 
R.3W. 

5 

i 

4 

T.4H. 
R.  3  E. 

T.  3N. 
R.2W. 

Ul 

3 

2 

BA 

SE 

1 

LI 

RE 

IV. 

Ill 

II. 

1. 

1 

II. 

III. 

IV.    * 

T.  2  S. 
R.2W. 

| 

2 

i 
j 

T.  ?  S. 
R.  3  E. 

T.  3S. 
R.  3W. 

1 

3 

C( 

RRECTI 

)N 

4 

III 

E 

T.  4  S. 
R.  4E. 

i 

120 


NEW   BUSINESS   ARITHMETIC 


and  Ohio  rivers;  the  third  starts  from  the  mouth  of  the  Ohio  and  runs 
north  to  the  northern  boundary  of  Illinois ;  the  fourth  begins  at  the  mouth 
of  the  Illinois  river  and  extends  north  through  Wisconsin  and  Minnesota, 
governing  surveys  in  Wisconsin,  Northern  Minnesota  and  Western  Illi- 
nois ;  the  fifth  begins  at  the  mouth  of  the  Arkansas  and  governs  surveys 
in  Arkansas,  Missouri,  the  greater  part  of  Minnesota  and  Dakota  east  of 
the  Missouri  river;  the  sixth  is  the  meridian  of  97  deg.  22  min.  west,  ex- 
tends south  to  latitude  37  deg.  and  north  to  the  Missouri,  and  controls 
the  surveys  in  Kansas,  Nebraska,  the  Dakotas  south  and  west  of  the 
Missouri,  Wyoming  and  all  of  Colorado  except  a  portion  along  the  Rio 
Grande,  which  is  surveyed  by  the  New  Mexico  meridian. 

Besides  these  there  are  eighteen  principal  meridians  in  the  United  States 
survey  known  by  names  instead  of  numbers.  These  are  the  Michigan  merid- 
ian, governing  surveys  in  Michigan;  the  Tallahassee,  St.  Stephens,  Hunts- 
ville,  Choctaw,  Washington  (Miss.),  St.  Helena  and  Louisiana  meridians 
governing  surveys  in  southern  states ;  the  New  Mexico  meridian,  longitude 
106  deg.,  52  min.,  9  sec. ;  the  Great  Salt  Lake  meridian,  the  Boise  meridian 
governing  surveys  in  Idaho;  the  Mount  Diablo  meridian,  121  deg.,  5  min. 
west,  governing  surveys  of  Central  and  Northeastern  California  and  all 
Nevada;  the  San  Bernardino  meridian  for  a  part  of  Southern  California, 
the  Humboldt  meridian  for  Northwestern  California,  the  Willamette 
meridian  for  Oregon  and  Washington;  the  Montana  meridian,  the  Gila 
and  Salt  River  meridian  for  Arizona  and  the  Indian  meridian  for  Indian 
Territory. 

N  178.  A   Base   Line    is   a    line 

which  crosses  the  principal  merid- 
ians at  right  angles  to  them,  and 
is  used  as  a  basis  of  measurements 
north  or  south. 

The  intersections  of  the  meridians 
and  base  lines  are  marked  by  substantial 
stone  monuments. 

Across  the   principal   meridians 
and  base  lines  at  right  angles,  other 
A  TOWNSHIP.  h'nes  are  run  six  miles  apart  which 


6 

5 

4 

3 

2 

1 

7 

8 

9 

10 

11 

12 

18 

17 

16 

15 

14 

13 

19 

20 

21 

22 

23 

24 

30 

29 

28 

27 

26 

25 

31 

32 

33 

34 

35 

36 

E 


S 


REDUCTION  OF  DENOMINATE  NUMBERS 


121 


N.  *. 

320  A 

N.W.fc 
of 
S.  W.& 
40  A. 

EH 
of 

S.  E.  &. 

S.W.J4 
of 

S.  W.& 
80^. 

160  A. 

S.W.M 

40^1. 

divide  the  territory  into  square 
tracts  six  miles  square.  These 
tracts  are  called  Townships. 

179.  Since  the  surface  of  the 
earth  is  convex,  all  meridians  con- 
verge as  the  latitude  increases; 
hence,  the  townships  and  sections 
are  not  exactly  rectangular,  which 
creates  a  necessity  for  occasional 
offsets  called  Correction  Lines. 
A  SECTION.  The  townships  are  numbered 

north  or  south  from  the  base  line.    Thus  "town  1  north,"  "town 

1  south,"  etc. 

180.  A  Range  is  a  line  of  townships  running  north   and 
south,  and  is  designated  by  its  number  east  or    west    from    the 
principal  meridian.     Thus  the  range  of  townships  lying  next  a 
prime  meridian  is  known  as  range  1,  east  or  west,  the  next  range 
2,  etc. 

181.  Each  township  is  divided  into  thirty-six  Sections,  each 
1  mile  square  and  containing  640  acres. 

These  sections  are  numbered  as  shown  in  the  accompanying 
diagram  beginning  at  the  N.  E.  cor.  and  running  W.  in  the  first 
tier,  E.  in  the  second,  etc.  All  fractional  sections  except  those 
due  to  lakes,  rivers,  and  other  natural  boundaries  are  thrown 
into  the  northern  and  western  rows.  Sections  are  further  divided 
into  halves,  quarters  and  eighths  or  forties. 

TABLE 
10000  square  links  make  1  square  chain . .  . .  sq.  ch. 

10  square  chains  1  acre A. 

640  acres  1  square  mile sq.  mi. 

36  square  miles  (6  mi.  sq.)  "     1  township Tp. 

1.  How  many  acres  in  a  township  of  land? 

2.  In  38  A.  8  sq.  ch.  240  sq.  1.  how  many  square  links  ? 

3.  Reduce  6525000  sq.  links  to  acres. 

4.  A  bought  a  farm  of  8584250  sq.  1.  at  $65  per  acre.    What 
did  the  farm  cost  him  ? 


122  NEW   BUSINESS   ARITHMETIC 

5.  A  sold  the  S.  W.  J  of  the  S.  E.  J  of  section  15  in  a  certain 
township  at  $87.50  per  acre.     How  much  did  he  receive  for  it? 
Locate  the  land  in  a  diagram. 

6.  Make  a  diagram  and  locate  B's  farm  of  40  acres  in    the 
E.  i  of  the  S.  4  of  the  N.  W.  i  of  sec.  29,  T.  3  N.  Range  2  W. 

7.  I  bought  a  half-quarter  section  of  land  at  $22  per  A.,  and 
sold  same  for  $26.15  per  A.    How  much  did  I  gain? 

8.  A  farmer  purchased  the  following  tracts  of  land :    N.  E.  J 
of  N.  E.  i,  S.  W.  i  of  N.  E.  i  at  $43.50  per  A. ;  N.  E.  i  of  S.  W. 
i,  S.  E.  i  of  N.  E.  i  at  $37.50  per  A. ;  N.  W.  i  of  S.  E.  J,  N.  E. 
I  of  S.  E.  i  at  $27.50  per  A.,  and  S.  E.  i  of  N.  W.  i,  N.  W.  J  of 
N.  E.  £  at   $31.25  per  A.    Find  the  cost  of  the  farm.    What  will 
it  cost  to  enclose  the  farm  with  a  board  fence  five  boards  high 
each  6  inches  wide  and  16  ft.  long  at  $16  per  M.  for  lumber  and 
$25  per  C.  for  posts,  same  to  be  placed  two  to  the  board  length? 
Draw  a  diagram  of  the  farm. 

9.  H's  farm  contains  the  following  pieces  of  land :  W.  -J  of  N. 
W.  JL,  W.  i  of  S.  W.  i,  E.  J  of  N.  E.  £,  E.  J  of  S.  E. 
i,  S.  4  of  S.  E.  i  of  N.  W.  i,  S.  J  of  S.  W.  i  of  N.  E.  i,  N.  J  of 
N.  E.  i  of  S.  W.  i,  N.  i  of  N.  W.  i  of  S.  E.  £.    How  many  acres 
of  land  in  his  farm  ?    Draw  diagram. 

10.  E  owns  the  following  described  property :    N.  W.  i  of  N. 
W.  i,  S.  W.  i  of  N.  W.    i,    N.    W.    i    of    S.    W.    i,    S.    W. 
i   of   S.    W.   i/  S.   E.    i   of   N.  W.  i,   S.   E.  i   of    S.  W. 
i,  N.  E.  i  of   N.    W.    i,    N.    W.  i    of    N.    E.    i   and    N.    E. 
J  of  N.  E.  i.    How  many  acres  does  he  own? 

11.  Draw  a  diagram  of  E's  land.     A  public  highway  is  laid 
out  on  the  N.,  W.  and  S.  sides  of  it  of  the  usual  width  (4  rods) 
one  half  on  E's  land.     How  many  acres  of  land  will  the  road 
occupy  on  his  land  ?    What  will  it  cost  to  fence  this  piece  of  land 
with  a  post  and  wire  fence,  posts  to  be  p/aced  one  to  the  rod  at 
$21  per  C  and  5  strands  of  wire,  each  strand  weighing  3  pounds 
to  the  rod  at  1  Jc  per  Ib.  ? 


REDUCTION     OF     DENOMINATE     NUMBERS 


123 


i  CUBIC  FEET 


A  RECTANGULAR  SOLID 
27  CU.  FT. 


III.    Cubic  Measure 

182.  Cubic  Measure  is  used  in  estimating  the  contents  of  solid 
bodies,  or  things  which  have  length,  breadth  and  thickness. 

183.  A  Rectangular  Solid  is  a  solid 
bounded  by  six  rectangular  sides. 

184.  A  Cube  is  a  rectangular  solid 
bounded  by  six  squares. 

A  Cubic  Inch  is  a  cube  each  dimen- 
sion of  which  is  1  inch.  A  Cubic  Foot 
is  a  cube  each  dimension  of  which  is  1 
foot.  A  Cubic  Yard  is  a  cube  each  di- 
mension of  which  is  1  yard. 

By  inspecting  the  figure  it  will  be 
readily  seen  that  3  cubic  feet  are  3  cubes 
of  1  foot  each,  and  a  cube  3  ft.  each  A  CUBE 

dimension  must  contain  27  such  cubes  or  27  cubic  feet. 

Hence  we  conclude,  that 

The  solid  contents  of  a  body  may  be  found   by  multiplying  its 
length,  breadth  and  thickness  together. 

TABLE 

1728  cubic  inches  (cu.  in.)  make  1  cubic  foot cu.  ft. 

27  cubic  feet  "       1  cubic  yard cu.  yd. 

128  cubic  feet  "       1  cord  of  wood C. 

NOTES. — 1.     In  measuring  wood  a  pile  8  feet  long,  4  feet  wide  and 
4  feet  high  is  called  a  cord. 

2.  A  cubic  yard  of  earth  is  called  a  load. 

3.  Railroad  and  transportation  companies   estimate  light   freight  by 
the  space  it  occupies  in  cubic  feet,  and  heavy  freight  by  weight. 

4.  A  perch  of  stone  or  of  masonry  is  \Ql/2  feet  long,  \l/2  feet  wide, 
and  1  foot  high. 

1.  Reduce  5  cu.  yd.  12  cu.  ft.  to  cu.  feet. 

2.  Reduce  3861  cu.  ft.  to  cords. 

3.  Find  the  number  of  cu.  ft.  in  a  solid  26  ft.  long,  2  ft.  wide 
and  iy2  ft.  thick. 

4-  Find  the  number  of  cu.  yd.  in  a  solid  25  yd.  long,  14  ft. 
wide  and  12  ft.  thick. 


124  NEW   BUSINESS   ARITHMETIC 

5.  Find  the  number  of  cu.  yd.  in  a  solid  12  yd.  long,  12  ft. 
thick  and  8  ft.  wide. 

6.  How  many  cords  are  there  in  a  pile  of  wood  28  ft.  long,  6 
ft.  high  and  4  ft.  wide  ? 

7.  At  $2.20  per  cord,  what  will  be  the  cost  of  a  pile  of  wood 
18  yd.  long,  6  ft.  high  and  2  ft.  wide? 

8.  How  many  cords  of  wood  can  be  put  into  a  building  16  ft. 
long,  12  ft.  wide  and  10  ft.  high? 

9.  How  many  cu.  ft.  of  water  will  a  cubical  cistern  hold, 
each  of  whose  dimensions  is  5  ft.  ? 

10.  What  will  it  cost  to  dig  a  cellar  21  ft.  long,  18  ft.  wide 
and  7  ft.  4  in.  deep,  at  40c  per  cu.  yd.? 

11.  I  bought  24  cords  of  wood  3  ft.  long,  and  put  it  in  a  pile 
8  ft.  high.    How  long  was  the  pile  ? 

12.  My  sleeping  room  is  12  ft.  long,  10  ft.  wide    and  9  ft. 
high.    If  I  breathe  10  cu.  ft.  of  air  in  one  minute,  in  how  long  a 
time  will  I  breathe  as  much  air  as  the  room  contains  ? 

18.  A  cellar  wall  is  112  ft.  long,  6  ft.  high  and  1|  ft.  thick. 
What  did  it  cost  at  $1.25  a  perch? 

14-  What  did  it  cost  to  dig  the  same  cellar,  its  length  being 
32  ft.,  at  15  cents  a  cubic  yard? 

15.  How  many  cubic  feet  in  a  wall  16  in.  thick,  38  ft.  long, 
and  30  ft.  high?  How  many  bricks  would  be  required  for  the 
above  wall  allowing  22  to  a  cubic  foot?  Wrhat  would  be  their 
value  at  $8.50  per  thousand? 

MEASURES  OF  CAPACITY 

185.  Measures  of  Capacity  are  those  which  determine  the 
quantity  of  matter  necessary  to  fill  a  given  space. 

186.  Measures  of  Capacity  embrace  Liquid  Measure  and  Dry 
Measure. 


REDUCTION   OF   DENOMINATE   NUMBERS  125 

I.    Liquid  Measure 
187.  Liquid  Measure  is  used  in  measuring  liquids. 

TABLE  ...    ,.. 

4    gills  (gi.)  make  1  pint pt. 

2    pints  1  quart qt. 

4    quarts  1  gallon gal. 

31 J :  gallons  1  barrel bbl. 

2    barrels,  or  63  gal.  1  hogshead . .  hhd. 

NOTES. — 1.  The  gallon,  which  contains  231  cu.  in.,  is  the  unit  of 
measure  in  liquids. 

2.  Casks  of  various  sizes  are  used  in  commerce,  called  tierces,  pipes, 
butts  and  tuns.  In  practical  business  each  cask  is  gauged  separately  and 
its  actual  contents  ascertained. 

1.  Reduce  13  gal.  to  pints. 

2.  Reduce  8  gal.  2  qt.  1  pt.  to  pints. 

3.  Reduce  5  hhd.  to  gills. 

4.  Reduce  5  gal.  3  qt.  1  pt.  3  gi.  to  gills. 

5.  Reduce  2  bbl.  16  gal.  1  pt.  to  pints. 

6.  Reduce  1270  pt.  to  gallons. 

7.  Reduce  13725  pt.  to  barrels. 

8.  How  many  barrels  in  10000  gallons? 

9.  What  will  be  the  cost  of  2  hhd.  of  wine  at  9c  a  gill  ? 

10.  A  merchant  bought  3  barrels  of  cider  vinegar  at  $5.25 
per  barrel  and  sold  it  at  8c  a  quart.    What  did  he  gain  ? 

11.  How  many  cans,  each  holding  3  qt.  1  pt.  3  gi.,  can  be 
filled  from  a  barrel  of  kerosene  oil  containing  42f  gal.  ? 

12.  How  many  cubic  inches  in  63  gal.? 

13.  How  many  gallons  in  4623  cu.  in.? 

14-  How  many  gallons  will  a  rectangular  cistern  hold,  which 
is  4  ft.  wide  6  ft.  long  and  8  ft.  deep? 

15.  How  many  gal.  of  water  will  a  cubical  cistern  hold,  each 
of  whose  dimensions  is  5  ft.? 

16.  How  many  gallons  of  water  may  be  put  into  a  cistern  6 
ft.  deep  and  4  ft.  square  at  the  top? 

17.  A  cistern  3  ft.  by  4  ft.  by  5J  ft.  is  f  full  of  water.    How 
many  gallons  does  it  contain? 


126  NEW   BUSINESS   ARITHMETIC 

Apothecaries  *  Fluid  Measure 

188.  Apothecaries'  Fluid  Measure  is  used  by  druggists  in 
compounding  liquid  medicines. 


TABLE 
60  minims  (TTL)  make    1  fluid  drachm,  marked    f3. 

8  £3  "1  fluid  ounce  "        £3. 

16  fS  "       1  pint,  "        O. 

8  O  "1  gallon,  "  cong. 


NOTES. — 1.  The  symbols  of  this  measure  precede  the  numbers  to 
which  they  refer.  Thus,  O4  £§6,  is  4  pints  6  fluid  ounces. 

2.  The  gallon  and  pint  of  this  measure  are  the  same  as  in  wine 
measure. 

1.  Reduce  O3  to  fj.- 

2.  Reduce  Oo  fJ12  to  f3. 

3.  Reduce  cong.l  O7  f§9  f35  to  fluid  drachms. 

4.  Reduce  cong. 3  Oo  £37  111,42  to  minims. 

5.  Reduce  1348  minims  to  higher  denominations. 

6.  Reduce  142860  Til  to  cong. 

II.    Dry  Measure 

189.  Dry  Measure  is  used  in  measuring  dry  articles  ;  as  grain 
fruit,  salt,  etc. 

TABLE 

2  pints  (pt.)  make  1  quart qt. 

8  quarts  1  peck pk. 

4  pecks  1  bushel bu. 

NOTE.— The  40-quart  or  "heaped"  bushel  is  used  for  apples,  pota- 
toes, etc.  Its  dimensions  are  18J4  inches  inside  and  8  inches  deep.  When 
heaped,  the  cone  must  not  be  less  than  6  inches  high,  and  it  contains 
2747.715  cubic  inches. 

NOTE. — The  standard  unit  of  Dry  Measure  is  the  bushel,  which  con 
tains  2150.42  cu.  inches. 

1.  Reduce  2  bu.  to  pints. 

2.  Reduce  5  bu.  3  pk.  to  pints. 

3.  Reduce  2  bu.  2  pk.  2  qt.  to  pints. 

4.  Reduce  7  bu.  3  pk.  7  qt.  1  pt.  to  pints. 


REDUCTION   OF   DENOMINATE   NUMBERS  127 

5.  Reduce  384  pt.  to  bushels. 

6.  Reduce  47  pt.  to  pecks. 

7.  Reduce  2865  pt.  to  bushels. 

8.  Reduce  11  bu.  3  pk.  7  qt.  1  pt.  to  pints. 

9.  What  will  2  bu.  of  nuts  cost  at  2-Jc  per  pint  ? 

10.  What  will  4  bu.  3  pk.  of  beans  cost  at  6c  per  quart  ? 

11.  WThat  will  2  pk.  4  qt.  of  cherries  cost  at  4fc  per  pint? 

12.  What  is  gained  by  buying  3  bu.  1  pk.  of  cherries  at  2Jc 
per  pint  and  selling  same  at  3Jc  per  pint? 

13.  A  merchant  bought  3  bu.  of  chestnuts  at  $1.20  per  bu., 
and  sold  the  same  at  3c  per  pint.    How  much  did  he  gain  ? 

14-  I  bought  .1  bu.  1  pk.  1  qt.  berries  at  2^c  per  pint  and 
sold  same  for  $2.46.  Find  the  total  cost,  and  the  selling  price  per 
quart. 

15.  How  many  cubic  inches  in  17  bushels? 

16.  How  many  bushels  in  15590.545  cu.  in.? 

17.  How  many  bu.  of  wheat  may  be  placed  in  a  bin  26  ft. 
long,  12  ft.  high  and  9  ft.  wide? 

18.  What  is  the  value  at  23c    per  bu.  of  potatoes  that  fill  a 
bin  18  ft.  5  in.  long,  7  ft.  8  in.  wide  and  6  ft.  9  in.  high  ? 

19.  At  35c    a  bushel,  what  is  the  value  of  oats  which  fill  a 
bin  16  ft.  long,  6  ft.  wide  and  4  ft.  high? 

20.  B  wishes  to  build  a  bin  that  will  hold  2000  bu.  of  corn. 
How  long  must  he  make  the  bin  if  it  is  16  ft.  wide  and  8  ft.  high? 

21.  A  wagon  whose  box  is  11  ft.  long,  3  ft.  6  in.  wide  and  2 
ft.  4  in.  high  is  filled  with  barley  worth  48c    per  bu.     Find  its 
value. 

22.  Wheat  worth  $120  at  75c  per  bu.  fills  a  bin  5  ft.  wide  and 
4  ft.  high.    Find  the  length  of  the  bin. 

Comparison  of  Dry  and  Liquid  Measures 

190.  The  Standard  Unit  of  Dry  Measure  is  the  bushel,  which 
contains  2150.42  cubic  inches. 

191.  The  Standard   Unit  of  Liquid  Measure  is  the  gallop 
which  contains  231  cubic  inches. 


128 


NEW   BUSINESS    ARITHMETIC 


COMPARATIVE  TABLE  OF  MEASURES  OF  CAPACITY 

LIQUID  MEASURE  DRY  MEASURE 

1  gallon  =  231    cu.  in.         268f  cu.  in. 
1  quart  =    57j  cu.  in.  67i  cu.  in. 

1  pint      =    28J  cu.  in.  33|  cu.  in. 

1.  Reduce  2  bu.  3  pk.  6  qt.  dry  measure  to  gallons  liquid 
measure. 

2.  Reduce  1  bbl.  20  gal.  1  qt.  to  dry  measure. 

3.  I  bought  2  bu.  1  pk.  1  qt.  of  nuts  by  dry  measure,  at  4c  per 
qt.     I  sold  same  at  4|c  per  qt.  by  liquid  measure.     How  much 
did  I  receive  and  what  was  my  gain? 

4'  I  bought  21  gal.  3  qt.  of  strawberries  liquid  measure  at  5c 
per  qt.  and,  sold  them  by  dry  measure  at  8c   per  qt.     Find  gain. 

5.  A  person  has  15  gal.  of  cherries  liquid  measure,  and  can  sell 
them  at  5c   per  qt.  liquid  or  7c   qt.  dry  measure.     Which  is  the 
"better  and  how  much  ? 

6.  A  bushel  or  32  quarts  dry  measure  contains  how  many 
.more  cubic  inches  than  32  quarts  liquid  measure? 

TIME 

192.  Time  is  a  measure  of  duration. 

The  Measures  of  Time  are  fixed  by  the  revolutions  of  the 
•earth  on  its  axis  and  around  the  sun. 

193.  A  Day  is  the  time  required  for  the  revolution  of  the 
earth  on  its  axis.    A  Year  is  the  time  required  for  the  revolution 

•of  the  earth  around  the  sun. 


60  seconds  (sec.) 
60  minutes 
24  hours 
7  days 

365  days  (52  weeks  1  day) 

366  days 

12  calendar  months 
100  years 


TABLE 

make  1  minute min. 

"       1  hour hr. 

"      1  day da. 

"       1  week wk. 

1  common  year.yr. 

1  leap  year yr. 

1  year yr. 

1  century C. 


NOTES. — 1.  The  exact  length  of  the  solar  year  is  365  days,  5  hours,  48 
minutes,  48  seconds;  but  is  usually  considered  to  be  365  days,  6  hours. 
Hence,  the  year  being  regarded  as  365  days,  the  odd  6  hours  of  each  year 


REDUCTION   OF   DENOMINATE   NUMBERS  129 

make  in  4  years  24  hours,  01  an  additional  day,  which  is  added  to  the 
shortest  month,  February,  and  gives  3G6  days  to  every  fourth  year,  called 
leap  year. 

2.     All    leap   years    are    divisible   by   4    and    all    centennial    years    not 
divisible  by  400  are  common  years. 

194.  The  year  is  divided  into  calendar  months  and  seasons 
as  follows: 

i  January  (Jan.) 31  days 
February  (Feb.) 28  days 
February  in  leap  year . .  .29  days 

(  March  (Mar.) 31  days 

SPRING ,  -j  April  (Apr.) 30  days 

(  May  (May) 31  days 

{June  (Jun.) 30  days 
July  (July) 31  days 
August  (Aug.) 31  days 

I  September  (Sept.) 30  days 

AUTUMN -J  October  (Oct.) 31  days 

(  November  (Nov.) 30  days 

WINTER December  (Dec.) 31  days 

The  number  of  days  in  each  calendar  month  may  be  easily  re* 
membered  by  committing  the  following  lines : 

"Thirty  days  hath  September, 
April,  June  and  November; 
All  the  rest  have  thirty-one, 
Save  February,  which  alone 
Hath  twenty-eight ;  and  one  day  more 
We  add  to  it  one  year  in  four." 

.?.  Reduce  2  hrs.  to  seconds. 

2.  Reduce  5  da.  8  hrs.  to  minutes. 

3.  Reduce  2  da.  7  hr.  45  min.  32  sec.  to  seconds. 
4-  Reduce  145  da.  5  hr.  27  min.  18  sec.  to  seconds. 

5.  Reduce  9  wk.  5  da.  15  hr.  25  min.  to  minutes. 

6.  Reduce  5  yr.  7  mo.  3  wk.  5  da.  16  hr.  42  min.  18  sec.  to 
seconds. 

7.  Reduce  14600  sec.  to  hours. 

S.  Reduce  26345  minutes  to  weeks. 

9.  -Reduce  41761  min.  to  months. 

10.  Reduce  12684500  sec.  to  higher  denominations. 

11.  How  many  days  are  there  from  March  18  to  July  1? 

12.  How  many  days  are  there  from  Nov.  26  to  Feb.  22  ? 
7-9.  How  many  days  are  there  from  June  1  to  Dec.  16? 
.I-/.  How  many  days  in  winter  in  a  leap  year? 

9 


130  NEW  BUSINESS   ARITHMETIC 

CIRCULAR  MEASURE 

195.  Circular  Measure  is  used  by  surveyors  in  determining 
directions,  by  navigators  in  fixing  the  location  of  vessels  at  sea 
and   by   astronomers   in   making   observations   on   the   heavenly 
bodies. 

Every  circle,  great  or  small,  may  be  said  to  be  divided  into 
360  parts  called  degrees,  consequently  the  length  of  a  degree  will 
vary  according  to  the  size  of  the  circle. 

196.  A  Degree  is  the  7J7  part  of  the  circumference  of  a 
circle. 


TABLE 

60  seconds    (")   make  1  minute ' 

60  minutes  "      1  degree ° 

30  degrees  "      1  sign S. 

12  signs  or  360°      "      1  circumference.  .C. 


NOTES. — 1.    A  degree  at  the  equator,  also  the  average  degree  of  lati- 
tude, is  equal  to  69.16  statute  miles. 

2.    Minutes  on  the  earth's  surface  are  called  geographic  miles. 

1.  Reduce  *4°  15'  36"  to  seconds. 

2.  Reduce  37°  48'  52"  to  seconds. 

3.  Reduce  12346"  to  higher  denominations. 

4.  How  many  degrees  are  there  in  J  of  the  circumference  of 
the  earth? 

•5.  How  many  degrees  in  5700  geographic  miles? 

6.  How  many  minutes  or  geographic  miles  in  a  semi-circum- 
ference of  the  earth  ? 

7.  How  many  statute  miles  in  180°  or  the  semi-circumference 
of  the  earth  ? 

8.  A  ship  was  driven  out  of  her  course  by  a  storm,  5°  15'  28". 
How  many  geographic  miles  was  this? 

197.  MISCELLANEOUS  TABLE 

12  things  =  1  dozen.  12  gross  =  1  great  gross. 

12  doze!?  =r  1  gross.  20  things  =  1  score. 


REDUCTION   OF   DENOMINATE   NUMBERS  131 

1.  What  cost  3  gross  pencils  at  4c  apiece? 

2.  A  bought  6  doz.  eggs  at  ISc   per  dozen.     Suppose  he  had 
paid  2c   apiece  for  them  how  much  more  would  they  have  cost? 

3.  A  merchant  bought  5  doz.  straw  hats  at  $5.45  per  dozen 
and  retailed  them  at  75c  each.    What  was  his  profit? 

PAPER 

24  sheets  =  1  quire  of  paper.  2  reams  =  1  bundle. 

20  quires  =  1  ream.  5  bundles  =  1  bale  or  case. 

The  terms  folio,  quarto,  octavo,  duodecimo,  etc.,  indicate  the 
number  of  leaves  into  which  a  sheet  of  paper  is  folded. 

STOCK    SIZES    OF    FLAT    OR    WRITING    PAPERS 

14  x  17  called  Cap.          18  x  23  called  Medium. 

16  x  21       "       Demy.       19  x  24       "       Royal. 

17  x  22       "       Folio.       17  x  28       "       Double  Cap. 

Most  flat  papers  are  now  furnished  500  sheets  to  the  ream  in- 
stead of  480  sheets,  as  formerly. 

STOCK    SIZES    OF    BOOK    PAPERS    FURNISHED    500    SHEETS 
TO    THE    REAM 

24  x  36  28  x  42  36  x  48 

25  x  38  32  x  44  38  x  50 

The  weight  of  papers  is  graded  as  so  many  pounds  per  ream. 
The  more  the  ream  weighs  the  heavier  each  individual  sheet  will 
be.  Paper  of  a  certain  size  and  weight  may  have  been  used  and  it 
is  often  desirable  to  know  the  weight  per  ream  of  an  equivalent 
sheet  but  of  another  size. 

4.  A  stationer  bought  1  bundle  of  note  paper  for  $12  and  sold 
it  at  the  rate  of  3  sheets  for  5c.    What  did  he  gain  ? 

5.  What  will  408  eggs  cost  at  28c  per  dozen? 

6.  Find  the  cost  of  5  great  gross  of  lead  pencils  at  3c  each. 

7.  How  old  is  a  person  who  is  three-score  and  five  years  old? 
S.  Find  the  weight  per  ream   of  the  equivalent  of  a   sheet 

24  x  36— 60#  in  25  x  38.    In  28  x  42. 

9.  Find  the  weight  per  ream  of  the  equivalent  of  a  sheet 
32  x  44— 80#  in  24  x  36.  In  25  x  38.  In  28  x  42. 


132  NEW    BUSINESS    ARITHMETIC 

10.  What  must  be  the  weight  of  a  ream  of  Cap  to  make  a  sheet 
equivalent  to  24#  Royal  ? 

11.  24#  Folio  would  be  what  in  Double  Cap? 

12.  28#  Royal  would  be  what  in  Folio? 

13.  16#  Cap  would  be  what  in  Royal? 

14.  What  would  be  the  weight  of  35  sheets  of  28#  Double 
Cap? 

15.  What  would  be  the  weight  of  16  sheets  of  40#  Royal? 

16.  An  untrimmed  book  has  512  pages  5J  x  7.     Out  of  what 
may  it  be  most  advantageously  run?     How  many  sheets  does  it 
take  for  each  book  ? 

17.  An  untrimmed  book  is  5£  x  8.    Out  of  what  will  it  cut  to 
best  advantage  ?    How  many  pages  to  each  sheet  ? 

18.  A  merchant  has  a  catalogue  3  x  9J  when  trimmed.     He 
wishes  to  bind  it  in  a  manila  cover  which  can  be  had  in  22%  x  28| 
— 90#  and  in  24  x  36— 100#.    Allowing  a  trim  of  %  in.  on  both 
top  and  bottom  and  J  in.  trim  on  sides,  how  many  covers  can  be 
cut  out  of  each  size  and  at  4{  cents  per  pound  which  is  the  most 
economical  size  to  use  ? 

REVIEW    PROBLEMS 

198.  1.  What  is  the  cost  of  3  bu.  plums  at  8c  a  qt.? 

2.  What  is  the  cost  of  4  bu.  3  pk.  peaches  at  40c  a  peck? 

3.  At  28c  per  pk.  how  many  bushels  of  apples  can  be  bought 
for  $36.96? 

4-  It  requires  8  yd.  3J  qr.  to  make  one  suit  of  clothes.    How 
many  suits  will  143  yards  make? 

5.  What  cost  1  Ib.  15  pwt.  of  silver  ore  at  2c  per  grain  ? 

6.  What  cost  3660  Ibs.  of  wheat  at  87|c  per  bushel? 

7.  How  many  spoons,  each  weighing  2  oz.  12  pwt.  can  be 
made  from  3  Ib.  8  oz.  4  pwt.  of  silver? 

8.  A  druggist  put  up  64  doz.  gr.2  quinine  powders.     How 
much  did  he  use  ? 

9.  If  one  bushel  of  wheat  will  make  45  Ib.  flour,  how  many 
barrels  of  flour  can  be  made  from  1000  bu.  of  wheat  ? 

10.  How  many  yd.  of  carpet  f  yd.  wide,  will  be  required  to 
cover  a  floor  27  ft,  long  and  18  ft.  wide? 


REDUCTION   OF   DENOMINATE   NUMBERS  133 

11.  At  30c   per  cord,  what  must  be  paid  for  sawing  a  pile  of 
wood  22  ft.  long,  7  ft.  high  and  4  ft.  wide  ? 

12.  I  paid  $10.50  for  a  barrel  of  pork.    How  much  is  that  a 
pound  ? 

13.  How  many  bu.  of  wheat  can  be  put  into  a  bin  7  ft.  4  in. 
long,  4  ft.  10  in.  wide  and  3  ft.  high? 

14.  What  must  be  the  length  of  a  bin  that  is  6  ft.  wide  and 
5  ft.  G  in.  high  to  contain  240  bu.? 

15.  If  a  family  use  4  Ib.  14  oz.  of  sugar  in  a  week  how  long 
will  1  cwt.  65  Ib.  12  oz.  last  them? 

16.  Find  the  cost  of  2  hhd.  wine  at  12c   per  pint. 

17.  The  human  heart  beats  70  times  a  minute.     How  many 
times  will  it  beat  in  a  day? 

18.  At  7Jc    per  cu.  ft,  what  will  be  the  cost  of  a  block  of 
stone  7  ft.  6  in.  long,  5  ft.  3  in.  wide  and  4  ft.  8  in.  thick  ? 

19.  At  50c    per  oz.,  what  is  the  value  of  a    silver    cup    that 
weighs  1  Ib.  5  oz.  7  pwt.  10  gr.  ? 

20.  At  $21  per  M.,  what  is  the  cost  of  3  sticks  of  timber  20 
ft.  long  and  18  in.  square  at  the  ends? 

21.  A  druggist  paid  50c  a  Ib.  Av.  for  potash  and  sold  same  in 
powders  of  3 1  gr.5  at  5c  each.    How  much  did  he  gain  on  10  Ib.  ? 

22.  A  cistern  is  7  ft.  long  5  ft.  wide  and  9  ft.  deep.     How 
many  hogsheads  of  water  will  it  contain  ? 

23.  How  many  square  feet  are  there  in  a  walk  around  the 
outside  of  a  rectangular  garden  which  is  100  feet  long  and  65  ft. 
wide,  the  walk  being  3  ft.  6  in.  wide? 

24.  How  many  boards  11^  ft.  long  and  10  in.  wide  will  be  re- 
quired for  the  flooring  of  a  room  17^  ft.  by  23  ft? 

25.  How  many  hours  longer  is  summer  than  autumn  ? 

26.  A  farmer  started  for  market  with  6  dozen  dozen  eggs; 
he  broke  half  a  dozen  dozen  and  sold  the  remainder  at  Ic  each. 
What  did  they  amount  to  ? 

27.  How  much  time  will  a  man  gain  in  60  yrs.  of  365  days 
by  rising  45  min.  earlier  every  day  than  his  usual  time? 

28.  How  many  cu.  ft.  in  a  stone  4  ft.  8  in.  long,  3  ft.    2    in. 
wide  and  2  ft.  thick  ?    How  many  sq.  ft.  on  its  surface  ? 


134  NEW  BUSINESS  ARITHMETIC 

29.  A  room  30  ft.  long  and  24  ft.  wide  is  covered  with  12G 
yd.  of  carpet.    What  is  the  width  of  the  carpet  ? 

30.  A  rectangular  field  containing  15  A.    is    350    rd.    long. 
How  wide  is  the  field?  , 

81.  A  cistern  7  ft.  long  and  5  ft.  wide  contains  105    cu.    ft. 
What  is  the  depth  of  the  cistern,  and  how  many  gal.  of  water 
will  it  hold  ? 

82.  What  will  be  the  cost  of  the  plank,  at  $15  per  M.,  that 
will  cover  a  floor  13  ft.  by  24  ft.,  if  the  plank  is  If  in.  thick? 

83.  How  many  dry  qt.  of  berries  may  be  put  into  a  cask  that 
contains  128J  wine  gallons,  and  what  are  they  worth  at  4£c   per 
qt? 

84.  Find  the  cost  of  10  pc.  2  by  4  in.,  10  pc.  2  by  6  in.,  15  pc. 
2  by  3J  in.,  12  pc.  2  by  7  in.,  if  the  pc.  are  12  ft.  long  and  the  cost 
is  $18.50  per  M. 

35.  How  many  tons  of  hay  of  320  cu.  ft.  each,  in  a  mow   40 
ft.  8  in.  long,  20  ft.  3  in.  wide  and  13  ft.  10  in.  high? 

36.  Allowing  320  sq.  ft.  for  doors  and  windows,  what  will  be 
the  cost  at  30c  per  sq.  yd.  of  plastering  a  room — the  ceiling  and 
walls — 42  ft.  6  in.  long,  26  ft.  3  in.  wide  and  14  ft.  high? 

37.  I  bought  14  bu.  3  pk.  by  dry  measure  at  $4  per  bu.,  and 
sold  the  same  at  18c   per  qt.  liquid  measure.    Did  I  gain  or  lose 
and  how  much  ? 

38.  My  silver  weighs  3  Ib.  7  oz.  by  the  scales  of  a  grocer; 
what  will  it  weigh  by  the  scales  of  a  jeweler? 

REDUCTION  OF  DENOMINATE  FRACTIONS 

199.  Reduction  of  Denominate  Fractions,  either  common  or 
decimal,  is  the  process  of  changing  them  to  equivalent  numbers  of 
different  denominations. 

Reduction  takes  place  in  two  ways :  From  a  higher  denomina- 
tion to  a  lower  by  multiplication.  From  a  lower  denomination  to 
a  higher  by  division. 

200.  To  reduce  a  denominate  fraction  to  lower  denomina- 
tions. 

1.  Reduce  f  of  a  bushel  to  lower  denominations. 


REDUCTION   OF   DENOMINATE   NUMBERS  135 

SOLUTION 

I  bu.  =  |  of  4  pk.  =  2^  pk. 
|  pk.  =  i  of  8  qt.  =  4  qt. 
Ans.  2  pk.  4  qt. 

From  this  solution  and  explanation  we  have  the  following : 

To  Reduce  Denominate  Fractions  to  Lower  Denominations 

a.  Multiply  the  fraction  by  that  number  which  will  reduce  it  to 
the  next  lower  denomination,  and  if  the  result  be  an  improper  frac- 
tion, reduce  it  to  a  whole  or  mixed  number. 

b.  Proceed  with  the  fractional  part,  if  any,  as  before,  until  re- 
duced to  the  denominations  required. 

c.  The  units  of  the  several  denominations,  arranged  in  their 
order,  will  be  the  required  result. 

NOTE. — If  after  multiplying  the  fraction  it  is  not  an  improper  fraction, 
proceed  to  reduce  it  to  the  next  lower  denomination  as  before. 

2.  Reduce  f  of  a  yard  to  lower  denominations. 

3.  Reduce  £  of  a  month  to  lower  denominations. 
4-  What  is  the  value  of  .45  of  a  gallon  ? 

SOLUTION 

.45  gal. 
4 


1.80  qt. 
2 


1.60  pt. 

4 

2.40  gi. 
1  qt.  1  pt.  2.4  gi.    Ans. 

5.  What  is  the  value  of  .26375  of  a  long  ton? 

6.  What  is  the  value  of  f  of  12  cwt.  ? 

7.  What  is  the  value  of  .725  of  16  acres? 

8.  What  is  the  value  of  3.48125  acres? 

P.  What  is  the  value  of  f  of  §  of  17£  bushels? 

10.  What  is  the  value  of  .165°  ? 

11.  Reduce  .8465  Ib.  apothecaries*  weight  to  lower  denomina- 
tions. 

12.  What  is  the  value  of  H  of  a  mile? 


136  NEW  BUSINESS  ARITHMETIC 

13.  Reduce  f  of  J  of  3  pounds  troy  to  lower  denominations. 

14-  Reduce  |  of  f  of  f  of  4  Ib.  avoirdupois  weight  to  lower  de- 
nominations. 

15.  A  grocer  disposed  of  .75  of  f  of  .175  of  a  hhd.  of  molas- 
ses. What  amount  was  that? 

201.  To  reduce  a  denominate  fraction  to  higher  denomina- 
tions. 

1.  Reduce  f  of  a  pwt.  to  the  fraction  of  a  pound. 

SOLUTION 

I x  £  x  £  =  ^ lbs- 

4 
Therefore  we  have  the  following: 

To  Reduce  Denominate  Fractions  to  Higher  Denominations 

a.  Divide  the  fraction  by  the  numbers  necessary  to  reduce  it  to 
the  denomination  required. 

NOTES. — 1.     Shorten  the  operation  by  cancellation  whenever  possible. 

2.  In  case  the  fraction  is  a  decimal  divide  as  in  division  of  decimals. 

2.  Reduce  f  pwt.  to  the  fraction  of  a  pound. 

3.  Reduce  §  of  a  cent  to  the  fraction  of  an  eagle. 
4..  Reduce  J  of  a  foot  to  the  fraction  of  a  mile. 

5.  Reduce  gr.f  to  the  fraction  of  a  pound. 

6.  Reduce  .25  of  a  pint  to  the  fraction  of  a  gallon. 
NOTE. — .25  pt.  =  ^fo  pt.  —  ^  pt.  and  then  proceed  as  before. 

7.  Reduce  f  pt.  to  the  fraction  of  a  peck. 

S.  Reduce  £  qt.  to  the  fraction  of  a  bushel. 
9.  Reduce  .125  oz.  to  the  fraction  of  a  T. 

10.  Reduce  .375  of  a  second  to  the  fraction  of  a  day. 

11.  Reduce  T7^  pt.  to  the  fraction  of  a  bushel. 

12.  Reduce  f   pt.  to  the  fraction  of  a  peck. 

13.  Reduce  {f  qt.  to  the  fraction  of  a  bushel. 

14-  i  °f  an  ounce  troy  is  what  fraction  of  3  pounds? 
15.  f  of  .675  pt.  is  what  fraction  of  6  bushels  ? 

202.  To  reduce  a  compound  number  to  a  fraction  of  a  higher 
denomination. 

1.  Reduce  5  da.  14  hr.  24  min.  to  the  fraction  of  a  week. 


REDUCTION   OF   DENOMINATE   NUMBERS  137 

SOLUTION 

5  da.  14  hr.  24  min.  =  8064  min. 
1  week  =  10080  min. 

Joei^JLwk. 

10080          5 
Therefore : 

To    Reduce    a  Compound  Number  to  a  Fraction  of  a  Higher 

Denomination 

a.  Reduce  the  compound  number  given  to  its  lowest  denomina- 
tion and  that  to  which  it  is  to  be  reduced  to  the  same. 

b.  Make  the  former  the  numerator,  and  the  latter  the  denomi- 
nator of  a  common  fraction,  which  reduce  to  its  lowest  terms. 

2.  Reduce  10  hr.  30  min.  to  the  fraction  of  a  da. 

3.  Reduce  215  rd.  3  yd.  2  ft.  10  in.  to  the  fraction  of  a  mile. 

4.  Reduce  1  brl.  1  gal.  1  qt.  1  pt.  1  gi.  to  the  fraction   of  a 
hogshead.  * 

5.  What  part  of  11  hhd.  is  4  gal.  1  qt.  1.28  pt.? 

6.  What  fraction  of  5  bushels  are  3  pk.  1  pt.  ? 

7.  What  part  of  6  ft.  square  is  6  sq.  ft.  ? 

8.  What  part  of  2  bu.  2  pk.  4  qt.  is  3  pk.  7   qt.  1  pt.? 

9.  What  part  of  9  ft.  square  is  9  sq.  inches? 
10.  What  part  of  3°  is  25"? 

203.  To  reduce  a  compound  number  to  Q  decimal  of  a  higher 
denomination. 

1.  Reduce  2  pk.  6  qt.  1  pt.  to  the  decimal  of  a  bu. 

SOLUTION 

2)1.0  pt. 
8)675000  qt. 
4)  2.812500  pk. 
.703125  bu. 
Therefore  we  may  prescribe  the  following: 

To  Reduce  a  Compound  Number    to    a    Decimal   of  a   Higher 

Denomination 

a.  Divide  the  lowest  denomination  given  by  that  number  which 
will  reduce  it  to  the  next  higher.    Prefix  the  next  higher  denomi- 


138  NEW   BUSINESS   ARITHMETIC 

nation  to  this  quotient.    Proceed  in  the  same  manner  until  the 
whole  is  reduced  to  the  denomination  required. 

2.  Reduce  8  oz.  15  pwt.  18  gr.  to  the  decimal  of  a  pound. 

3.  Reduce  1  hr.  12  min.  18  sec.  to  the  decimal  of  a  day. 

4.  Reduce  5  minutes  to  the  decimal  of  a  day. 

5.  What  decimal  of  a  peck  is  7  qt.  1  pt.  ? 

6.  What  decimal  of  a  bushel  is  2  pk.  3  qt.  1  pt.  ? 

7.  What  decimal  of  a  fathom  is  3f  feet? 

8.  What  decimal  of  3  miles  is  .3  feet? 

9.  What  decimal  of  a  barrel  of  flour  is  18.25  Ibs.? 

10.  Reduce  5  sq.  yd.  7  sq.  ft.  80  sq.  in.  to  the  decimal  of  an 
acre. 

11.  Reduce  5A.  60  sq.  rd.  25  sq.  yd.  to  acres  and  decimals 
thereof. 

REVIEW    PROBLEMS 

204.  1.  What  will  be  the  cost  of  5  brls.  75  Ibs.  of  flour   at 
$6.50  per  barrel  ? 

2.  What  cost  18  bu.  3  pk.  5  qt.  of  corn  at  45c  per  bushel  ? 

3.  What  will  45A.  122  sq.  rd.  18  sq.  yds.  of  land  cost  at 
$450  per  acre  ? 

4.  8  gal.  3  qt.  1  pt.  3  gi.  are  what  part  of  a  hogshead  ? 

5.  A  jeweler  sold  10  oz.  5  pwt.  8  gr.  of  plated  ware  at  the 
rate  of  $2.40  per  Ib.    How  much  did  he  receive? 

6.  At  $59.25  per  acre,  how  much  land  can  be  bought  for 
$1285.40? 

7.  It  cost  $267.30  to  build  a  mile  of  fence.     What  will  it 
cost  to  fence  both  sides  of  a  railroad  17  mi.   135   rd.   3J  yd. 
long? 

8.  Reduce  5  cwt.  68  Ib.  12  oz.  14  dr.  to  the  decimal  of  a  ton. 

9.  How  much  greater  is  the  area  of  a  lot  25  rds.  square, 
than  a  lot  containing  25  sq.  rds.  ? 

10.  In  .5  hhd.  .8  gal.  .02  qt.  how  many  pints? 

11.  What  decimal  of  6  mi.  is  3  rd.  5  yd.  2  ft.  7  in.? 

12.  Find  the  cost  of  a  farm  80  ch.  long  and  33  ch.  50  1.  wide, 
at  $36.50  per  A. 

J5.  Reduce  7  hr.  24  min.  18.625  sec.  to  the  decimal  of  a  year. 


REDUCTION   OF   DENOMINATE   NUMBERS  139 

14.  How  many  times  does  a  wheel,  14  ft.  8   in.   in  circumfer- 
ence, turn  around  in  going  a  distance  of  10  miles  ? 

15.  If  a  person  could  travel  a  second  of  distance  in  a  second 
of  time,  how  long  would  be  required  to  go  entirely  around  the 
earth? 

16.  How  many  seconds  shorter  is  autumn  than  spring? 

17.  At  $21.75  per  rod,  what  will  it  cost  to  grade  a  road   23 
mi.  172  rd.  long? 

18.  A  bill  of  goods  amounts  to  £46  6s. ;  change  to  U.  S.  money. 

19.  An  invoice  totals  £176  6s.  7d. ;  change  to  U.  S.  money. 

20.  A  purchase  amounts  to  $271.64;  change  to  English  money. 

21.  An  invoice  totals  £426  5s.,  tariff  $145.60,  freight  $90.63. 
What  is  the  total  in  U.  S.  money  ? 

22.  Bought  220  yards  of  cloth  at  £1  9s.  2d.  per  yard.    What  is 
the  cost  U.  S.  money  ? 

23.  A  Liverpool  clerk  receives  £960  per  year,  one  in  Boston 
receives  $3,000.    Which  receives  the  larger  salary  and  how  much 
in  U.  S.  money? 

24.  A  Philadelphia  merchant  receives  four  invoices  of  goods 
purchased  at  foreign  points,  viz: 

A  bill  from  Sheffield  amounting  to  £245  6s. 
A  bill  from  Paris  amounting  to  1463.7  fr. 
A  bill  from  Hamburg  amounting  to  2164.8  m. 
A  bill  from  St.  Petersburg  amounting  to  2243.9  rubles. 
Find  the  total  of  the  four  bills  in  U.  S.  currency. 

ADDITION 

205.  The  process  of  uniting  numbers  of  different  denomina- 
tions is  termed  Addition  of  Compound  Numbers. 

1.  Add  16  bu.  2  pk.  4  qt. ;  11  bu.  3  pk.  5  qt.  1  pt. ;  8  bu.  1  pk. 
Ipt.  • 

SOLUTION 
482 

bu.    pk.    qt.    pt. 
16       2       4       0 
11       3       5       1 
8101 
36       3       2       0 


140  NEW    BUSINESS   ARITHMETIC 

From  this  solution  and  explanation  we  have  the  following: 

To  Add  Compound  Numbers 

a.  Write  the  numbers  so  that  those  of  the  same  unit  value  will 
stand  in  the  same  column. 

b.  Beginning  at  the  right  hand,  add  each  denomination  as  in 
simple  numbers,  carrying  to  each  succeeding  denomination  one  for 
as  many  units  as  it  takes  of  the  denomination  added  to  make  one 
of  the  next  higher  denomination. 

NOTES. — 1.  Reduce  denominate  fractions,  if  any,  to  integers  of  lower 
denominations  and  then  add. 

2.  It  may  be  helpful  to  the  student  to  write  the  numbers  of  the  table 
above  the  columns  before  beginning  the  addition. 

Find  the  sum  of  the  following : 


(2) 

(B) 

20 

12 

4 

20 

100 

16 

16 

L 

S. 

d. 

far. 

T. 

cwt. 

Ib. 

oz. 

dr. 

6 

14 

8 

3 

2 

12 

65 

10 

15 

5 

7 

9 

2 

3 

8 

42 

5 

0 

16 

4 

0 

1 

5 

15 

84 

11 

12 

11 

18 

2 

3 

2 

6 

32 

0 

8 

38       43     19       9  12       41     223       26       35 

4.  A  fanner  sold  six  loads  of  wheat  as  follows :    23  bu.  3  pk. 
7  qt.  1  pt. ;  26  bu.  2  pk.  5  qt. ;  18  bu.  5  qt.  1  pt;  32  bu.  3  pk.  5 
qt. ;  38  bu.  3  pk.  7  qt.  1  pt.  and  36  bu.  3  pk.  1  pt.    What  was  the 
entire  amount? 

5.  What  is  the  sum  of  3  mi.  180  rd.  3  yd.  1  ft.  10  in. ;  .5  mi. 
246  rd.  4  yd.  2  ft.  9  in. ;  16  mi.  148  rd.  2  yd.  2  ft.  8  in.  and  30S 
rd.  4  yd.  2  ft.  1  in.  ? 

6.  A  man  has  three  farms.    The  first  contains  87  A.  116  sq. 
rd.  25  sq.  yd.  4  sq.  ft.  76  sq.  in. ;  the  second  64  A.  84  sq.  rd.  30 
sq.  yd.  8  sq.  ft.  127  sq.  in.;  the  third  128  A.  100  sq.  rd.  16  sq. 
yd.  6  sq.  ft.  42  sq.  in.    How  much  land  has  he  in  all  ? 

7.  A  ship  leaving  Boston  sailed  east  the  first  day  3°  25'  42" ; 
the  second  day  3°  14'  7";  the  third  day  2°  58'  16";  the  fourth 
day  3°  36'  14"  and  the  fifth  day  4°  2'   18".    How   far  was   she 
then  east  of  the  port  of  Boston  ? 


REDUCTION   OF   DENOMINATE   NUMBERS  141 

S.  A  farmer  sold  5  loads  of  shelled  corn  at  42c  per  bushel, 
weighing  respectively  3248,  2846,  3514,  2954  and  3015  pounds. 
\Yhat  did  he  receive  for  all  ? 

9.  What  is  the  sum  of  14  hhd.  28  gal.  1  qt.  1  pt. ;  23  hhd. 
16  gal.  3  qt.  1  pt. ;  f  hhd. ;  15  hhd.  18  gal.  3  qt.  ? 

NOTE. — Reduce  the  §  hhd.  to  integers  of  lower  denominations  accord- 
ing to  Art.  202  and  then  add  as  before. 

10.  Add  f  of  a  mile;  13J  rd.  and  148  rd.  7  ft.  8  in. 

11.  Sold  four  town  lots.    The  first  contained  2  A.  84   sq.  rd. ; 
the  second  3  J  A. ;  the  third  f  of  an  acre ;  and  the  fourth  f  of  f 
of  300  sq.  rds.    How  much  land  in  all  ? 

SUBTRACTION 

206.  The  process  of  finding  the  difference  between  two  num- 
bers having  two  or  more  denominations  is  termed  Subtraction  of 
Compound  Numbers. 

1.  From  12  bu.  2  pk.  3  qt.  subtract  8  bu.  3  pk.  5  qt. 

SOLUTION 
4  8 

bu.    pk.    qt. 
12       2       3 

835 

3       2       6 

We  may  therefore  give  the  following : 

To  Subtract  Compound  Numbers 

a.  Write  the  less  number  under  the  greater  and  units  of  the 
same  denomination  in  the  same  column. 

b.  Subtract  the  lower  number  from  the  upper  if  possible. 

c.  But,  if  the  lower  number  of  any  order  be  greater  than  the 
upper,  increase  the  upper  number  by  as  many  units  of  that  denom- 
ination as  make  one  of  the  next  higher;  subtract  as  before,  and 
carry  one  to  the  loiver  number  of  the  next  higher  order.    Proceed 
in  the  same  manner  with  each  denomination. 

NOTE. — In  simple  subtraction,  when  any  lower  figure  is  greater  than 
the  upper,  we  borrow  ten,  ten  units  of  a  lower  order  making  a  unit  of  the 
iic.rt  higher.  In  Compound  Numbers,  when  the  lower  number  of  any 


142  NEW   BUSINESS   ARITHMETIC 

order  is  greater  than  that  above  it,  borrow  the  number  of  units  in  that 
order  which  makes  a  unit  of  the  next  higher. 
Subtract  the  following : 

(2)  (3) 

12  20  24  365  24  60  6G 

lb.     oz.     pwt.     gr.  yr.       da.       hr.     min.     sec. 

16      8        14        7  46       218       16       28       56 

49        10      16  13       310         5       42       37 

4.  A  bin  contains  65  bu.  of  wheat.    If  7  bu.  3  pk.  5  qt.  1  pt. 
are  taken  out  how  much  will  remain  ? 

5.  From  a  hhd.  of  molasses  there  leaked  out  7  gal.  3  qt.  1  pt. 
3  gi.    How  much  remained  ? 

6.  A  wagon  loaded  with  hay  weighed  3  T.  4  cwt.  18  lb.  13 
oz.     The  wagon  alone  weighed  8  cwt.  24  lb.  7  oz.     How  much 
did  the  hay  weigh  ? 

7.  A  New  York  merchant    owed    a    London    manufacturer 
£628  15s.  8d.  3  far.  for  goods  bought.     He  paid  him  £265  10s. 
9d.  2  far.    How  much  did  he  still  owe  ? 

8.  A  section  of  land  is  owned  by  three  men.    The  first  owns 
256  A.  125  sq.  rd.  15  sq.  yd. ;  the  second  185  A.    64    sq.    rd.    22 
sq.  yd.  6  sq.  ft.,  and  the  third  the  remainder.     How  much  land 
did  the  third  man  own? 

9.  How  many  weeks,  days,  hours  and  minutes    are    there 
from  15  min.  after  noon  on  April  1,  to  48  minutes  before  midnight 
on  September  26? 

SOLUTION 
30       24        60 

mo.  da.  hr.  min. 

9     26     23     12 

4  1     12     15 

5  25     10     57 

10.  Find  the  time  from  October  30,  1892,  to  May  21,  1895. 

11.  A  note  dated  December  16,  1895,  was  paid  on  August  4, 
1896.    How  long  did  it  run? 

12.  Take  3  qr.  16  sheets  of  paper  from  1  bundle  of  paper. 

13.  A  ship  starts  at  south  latitude  12°  42'  38"  and  sails  to 
south  latitude  60°.    Through  what  distance  has  she  sailed? 


REDUCTION   OF   DENOMINATE   NUMBERS  143 

14-  What  length  of  time  elapsed  from  10  a.  m.  on  September 
20,  1893,  to  3  p.  m.  on  May  6,  1895? 

15.  From  12  cwt.  85  Ib.  take  -ft-  of  a  ton. 

NOTE. — Reduce  the  fractions  to  lower  denominations. 

16.  From  8T%  wk.  take  5|  da. 

17.  From  a  cask  containing  42  gal.  of  brandy  J  leaked  out 
and  J  of  the  remainder  was  sold.    How  much  still  remained?- 

MULTIPLICATION 

207.  The  process  of  taking  a  number  consisting  of  different 
denominations  a  certain  number  of  times  is  called  Multiplication 
of  Compound  Numbers. 

1.  Multiply  7  bu.  2  pk.  3  qt.  1  pt.  by  5. 

SOLUTION 
4         8 

bu.  pk.  qt.  pt. 

7251 

3      v*     5 

38      1      31 

Therefore, 

To  Multiply  Compound  Numbers 

a.  Write  the  multiplier  under  the  lowest  denomination  of  the 
multiplicand. 

b.  Multiply  as  in  simple  numbers  and  carry  as  in  addition  of 
compound  numbers. 

NOTE. — We  multiply  the  lowest  denomination  first  so  as  to  carry  from: 
a  lower  to  a  higher. 

(*)  (s) 

12  20  24 

bu.     pk.     qt.     pt.  Ib.       oz.       pwt.       gr. 
5       3     V       1  3         8         16         20 
3      7*  9 


4.  A  farmer  owns  5  fields  each  containing  68  A.  86  sq.  rd. 
sq.  yd.  7  sq.  ft.  65  sq.  in.    How  much  land  has  he  in  all  ? 


144  NEW    BUSINESS    ARITHMETIC 

5.  How  many  gallons  in  5  casks  each  containing  18  gal.  3  qt. 
1  pt.  3  gi.  ? 

6.  A  laborer  excavates  2  cu.  yd.  5  cu.  ft.  41(1  cu.  in.  of  earth 
in  one  day.     How  much  will  he  excavate  in  17  days  at  the  same 
rate? 

7.  What  will  be  the  weight  of  23  loads  of  hay,  each  weigh- 
ing 4  T.  6  cwt.  38  Ib.  14  oz.  ? 

DIVISION 

2O8.  The  process  of  finding  how  many  times  a  given  num- 
ber is  contained  in  another  number  consisting  of  different  denom- 
inations is  called  Division  of  Compound  Numbers. 

1.  Divide  13  da.  T  hr.  25  min.  45  sec.  by  5. 

SOLUTION 

24  60  60 

da.     hr.     min.     sec. 
5)13       7       25         45 
2     15       53~    ~9 

Therefore  we  have  the  following : 

To  Divide  Compound  Numbers 

a.  Begin  at  the  left  hand  and  divide  the  highest  denomination 
of  the  dividend  by  the  divisor,  and  write  the  quotient  beneaih. 

b.  If  there  be  a  remainder  after  the  division  of  any  portion  of 
the  dividend,  reduce  the  remainder  to  the  next  lower  denomina- 
tion, add  to  it  the  number  belonging  to  that  denomination,  if  any, 
and  divide  as  before. 

c.  Continue  to  divide  in  this  manner  until  the  entire  dividend 
has  been  used. 

NOTE. — We  begin  at  the  left  hand  in  order  to  reduce  the  remainders 
to  lower  denominations  and  thus  finally  succeed  in  dividing  them. 

(e)  (s) 

482  12         8  3  20 

bu.     pk.    qt.     pt.  Ib.        3.      3.      3.     gr. 

7)25       3       5       1  9)17       1       0       2       18 

4-  A  railroad  train  runs  1000  mi.  in  26  hours.    What  rate  is 
that  per  hour  ? 


REDUCTION   OF   DENOMINATE   NUMBERS  145 

5.  Seventeen  barrels  of  sugar  weigh  2  T.  6  cwt.  34  Ib.  8  oz. 
What  is  the  average  weight  ? 

G.  A  man  owning  -J-  a  section  of  land  left  it  to  his  3  sons 
equally.  How  many  acres  should  each  receive? 

7.  A  silversmith  made  half  a  dozen  silver  spoons  weighing 
2  Ib.  8  oz.  10  pwt.    What  was  the  weight  of  each  ? 

8.  A  farmer  raised  846  bu.  3  pk.  5  qt.  of  wheat  in  a  field  of 
16  acres.    How  much  was  that  per  acre  ? 

9.  A  family  consumes  10  bbl.  of  flour  in  a  year.     What  is 
the  average  amount  each  day? 

10.  A  cellar  45  ft.  long,  30  ft.  wide  and  6  ft.  deep,  was  ex- 
cavated by  5  men  in  6  days.  How  many  cubic  yards  did  each 
man  excavate  daily  ? 


10 


LONGITUDE  AND  TIME 

209.  Longitude  is  the  distance  east  or  west  from  an  estab- 
lished point  or  meridian  on  the  earth's  surface. 

Nations  usually  fix  their  own  capital  or  national  observatory 
as  the  point  from  which  to  measure  longitude,  but  in  the  United 
States  it  is  quite  customary  to  reckon  from  the  observatory  at 
Greenwich,  England. 

210.  Standard  Time  is  the  sun  time  of  some  selected  meridian 
of  longitude.    Solar  Time  is  the  sun  time,  mid-day  occurring  at  a 
given  place  when  the  sun  reaches  the  meridian  of  that  place,  thus, 
there  is  a  different  time  for  every  meridian.     The  standard  time 
was  adopted  to  avoid  the  necessary  confusion  caused  to  travel- 
ers and  others   by  the  difference  of  time.     Railroads  and  many 
cities  and  towns  have  adopted  standard  time. 

In  the  United  States  eastern  standard  time  is  the  sun  time  of 
the  meridian  75°  west  of  Greenwich;  central  standard  time,  90°  ; 
mountain  standard  time,  105° ;  western  (Pacific)  standard  time, 
120°.  The  standard  time  is  one  hour  earlier  in  the  day,  in  each 
successive  belt  toward  the  west;  and  one  hour  later  in  the  day, 
in  each  successive  belt  toward  the  east.  Thus,  when  it  is  11  a. 
m.  in  the  Eastern  belt — 7-J°  on  each  side  of  the  75th  meridian — it 
is  10  a.  m.  in  the  Central  belt,  9  a.  m.  in  the  Mountain  belt,  8  a. 
m.  in  the  Western  belt. 

Every  circle,  great  or  small,  may  be  considered  as  divided 
into  360  equal  parts  called  degrees.  Since  the  earth  turns  on  its 
axis  once  in  24  hours,  a  point  on  the  earth's  surface  will  describe 
a  circumference  (360°)  in  24  hours;  in  1  hr.,  the  point  would 
describe  •£%  of  360°  or  15°  ;  in  1  min.,  the  point  would  describe 
^V  of  15°  or  15';  in  1  sec.,  the  point  would  describe  ^V  °f  15''  or 
15". 

Therefore  we  have  the  following : 

TABLE  OF  COMPARISON  BETWEEN  LONGITUDE  AND  TIME 
15°  of  longitude  =  1  hour  of  time. 
15'   of  longitude  =  1  min.  of  time. 
15"  of  longitude  =  1  sec.  of  time. 
146 


LONGITUDE   AND   TIME 


147 


The  following  table  showing  the  longitude  of  important  cities 
of  the  world  east  or  west  from  Greenwich,  England,  will  be  used 
in  the  solution  of  the  problems : 


TABLE  OF  LONGITUDES 


Place 

Longitude 

Place 

Longitude 

Portland  Me     .   . 

o       /     // 
70  15  18  V 

I 

St  Louis   Mo 

O         i       n 

90  12  14  \V 

Boston    Mass  .... 

71    3  40 

Minneapolis    Minn 

93  14    8 

New  Haven  Conn. 

72  55  45 

Des  Moines  la  

93  37  16 

New  York  City.  .  . 

74    0  24 

Omaha,  Neb  :  .  .  . 

95  56  14 

Philadelphia,  Pa.  . 

75    9    3 

Austin,  Tex  

97  44  12 

Baltimore,  Md.  ... 

76  36  59 

Denver,  Colo  

104  59  33 

Washington,  D.  C. 
Richmond,  Va.  ... 

77    0  15 
77  26    4 

Salt  Lake  City,  Utah  
San  Francisco,  Cal  

111  53  47 

122  27  49 

Charleston  S  C 

79  55  40 

Sitka  Alaska. 

135  19  42 

Pittsburg  Pa 

80    2    0 

Rio  Janeiro    Brazil 

43  20    0 

Savannah  Ga.  .  .  . 

81     5  26    * 

t 

Honolulu   Sandwich  Is 

157  52    0 

Detroit  Mich  

83    3    0 

( 

Paris    France  

2  20    0   E 

Cincinnati  O  .... 

84  29  45 

t 

Rome,  Italy  

12  28    0 

Louisville,  Ky.  .  .  . 
Indianapolis,  Ind. 

85  25    0 
86    6    0 

* 

Berlin,  German  Empire. 
Vienna,  Austria  

13  23    0 
16  20    0 

Nashville,  Terin.  .  . 
Chicago,  111  

86  49    0 

87  35    0    ' 

i 

Constantinople,  Turkey. 
St.  Petersburg,  Russia.  . 

28  59    0 
30  16    0 

M^obile  Ala 

88    2  28     ' 

Bombay  India 

72  48    0 

Madison  Wis 

89  24    3    ' 

Pekin   China 

116  26    0 

New  Orleans,  La.  . 

90    3  28    ' 

' 

Sydney,  Australia  

151  11    0 

1.  The  difference  in  longitude  between  two  places  is  18 ( 
30".    What  is  the  difference  in  time  ? 


25' 


SOLUTION 

60  60 

15)18°     25'  30" 

1       13  42 


EXPLANATION.— By  reference  to  the  table  of 
comparison  on  the  previous  page  we  see  that 
15°  equal  an  hour  of  time,  15'  equal  1  min.  of 
time  and  15"  equal  1  second  of  time.  There- 
fore 18°  25'  30"  will  be  equal  to  as  many  hours, 

minutes  and  seconds  as  15  is  contained  in  them,  and  dividing  according  to 
the  rules  for  division  of  Compound  Numbers  we  have  as  a  result  1  hr.  13 
min.  42  sec. 

From  the  foregoing  we  have  the  following: 

To  Change  Longitude  to  Time 

a.  Divide  the  longitude  by  15  according  to  the  rule  for  division 
of  Compound  Numbers  and  the  result  will  be  time. 

Since  the  reverse  of  division  is  multplication,  we  may  reduce 
time  to  longitude  by  the  following : 


148  NEW   BUSINESS   ARITHMETIC 

To  Change  Time  to  Longitude 

a.  Multiply  the  time  by  15  according  to  the  rule  for  multiplica- 
tion of  Compound  Numbers  and  the  result  will  be  longitude. 

NOTE.— If  one  place  be  in  east,  and  the  other  in  west  longitude,  the 
difference  of  longitude  is  found  by  adding  them,  and  if  the  sum  be  greater 
than  180%  it  must  be  subtracted  from  360°. 

2.  The  difference  of  longitude  between  two  places  is  30°. 
What  is  the  difference  of  time  ? 

3.  The  difference  of  longitude  between  two  cities  is  16°  34'. 
What  is  the  difference  of  time  ? 

4.  The  difference  of  longitude  between  New  York  and  Chi- 
cago is  13°  11'.    What  is  the  difference  in  time? 

5.  The  difference  of  time  between  two  places  is  2  hr.  30  min. 
What  is  the  difference  of  longitude  ? 

6.  The  difference  of  longitude  between  London  and  Wash- 
ington is  77°  0'  15".    What  is  the  difference  in  time? 

7.  What  is  the  difference  in  time  between  Portland,  Me.,  and 
New  Orleans? 

8.  What  is  the  difference  of  time  between  Richmond,  Va., 
and  Des  Moines,  la.  ? 

9.  What  is  the  difference  in  time  between  Detroit,  Mich.,  and 
San  Francisco,  Cal.? 

10.  What  is  the  difference  in  time  between  Nashville,  Tenn., 
and  Omaha,  Neb.  ? 

11.  What   is   the   difference   in   time   between   New   Haven, 
Conn.,  and  Denver,  Colo.? 

12.  What  is  the  difference  in  time  between  New  York  and 
Sitka,  Alaska  ? 

13.  What  is  the  difference  in  time  between  Rio  Janeiro,  Bra- 
zil, and  Honolulu,  Sandwich  Islands  ? 

14.  What  is  the  difference  in  time  between  Rome,  Italy,  and 
Boston,  Mass.  ? 

15.  When  it  is  noon  at  Charleston,  S.  C,  what  is  the  time  at 
Indianapolis,  Ind.  ? 

NOTE. — Since  Charleston  is  east  of  Indianapolis,  subtract  the  differ- 
ence of  time. 


LONGITUDE   AND   TIME  149 

16.  When  it  is  2  p.  m.  at  St.  Louis,  Mo.,  what  is  the  time  at 
Philadelphia,  Pa.  ? 

NOTE. — Since  St. 'Louis  is  west  of  Philadelphia,  add  the  difference  of 
time  to  2  p.  m. 

17.  When  it  is  noon  at  Chicago  what  is  the  time  at  Rome, 
Italy? 

NOTE. — Since  Chicago  is  west  and  Rome  east  of  the  prime  meridian, 
the  difference  between  their  longitudes  is  found  by  taking  the  sum  of 
their  longitudes.  Since  Rome  is  east  of  Chicago,  the  difference  of  time 
is  added  to  the  time  of  Chicago  to  find  the  time  at  Rome. 

18.  When  it  is  1  p.  m.  at  Omaha  what  is  the  time  at  Paris, 
France  ? 

19.  What  is  the  time  of  day  at  Berlin  when  it  is  2  p.  m.  at 
New  York? 

20.  When  it  is  midnight  at  Boston  what  is  the  time  at  Austin, 
Texas  ? 

21.  What  is  the  time  of  day  at  Washington  when  it  is  28 
min.  past  10  a.  m.  at  Chicago? 

22.  St.   Petersburg  is  east  longitude  and   St.   Louis  is  west 
longitude.     When  it  is  1  a.  m.  at  St.   Petersburg,  what  is  the 
time  at  St.  Louis? 

23.  When  it  is  1  a.  m.  on  Wednesday  at  Washington  what 
is  the  time  at  Bombay?    When  it  is  10  min.  past  2  a.  m.  on  Sun- 
day at  Bombay  what  is  the  time  at  Washington  ? 

211.  The  International  Date  Line  is  an  imaginary  line,  in 
crossing  which  navigators  must  either  add  or  subtract  a  day  in 
order  to  make  their  calendar  correspond  to  that  of  the  inhabitants 
of  the  adjacent  islands. 

Given  the  time  of  day  and  longitude  of  one  place  and  the 
longitude  of  another,  and  the  time  of  day  of  the  latter  is  easily 
found  but  to  find  the  correct  day  of  the  month  is  not  always  so 
easy.  For  this  purpose  a  knowledge  of  the  "International  Date 
Line,"  a  cut  of  which  is  given  on  the  following  page  is  indispens- 
able. 

Travelers  in  going  round  the  earth  to  the  west  find  themselves  a  day 
behind  the  calendar  and  when  going  east,  a  day  ahead,  irrespective  of  the: 
time  required  to  make  the  trip. 


150 


NEW   BUSINESS   ARITHMETIC 


Starting  from  somewhere  in  Asia  the  world  has  been  peopled  by  some 
going  east  and  some  going  west.  These  tides,  as  it  were,  of  people  met 
in  the  Pacific  ocean,  Asia  and  a  few  islands  along  the  coast  being  peopled 
by  those  coming  from  the  west  and  America  with  the  islands  in  the  eastern 
Pacific  by  those  coming  from  the  east.  Each  branch  brought  its  own  time 
and  when  they  met  they  must  necessarily  differ  by  a  full  day.  The  "Inter- 
national Date  Line"  represents  where  they  met  and  hence  marks  the 
division  between  the  two  kinds  of  time.  On  one  side  of  the  line  it  is 


LONGITUDE   AND   TIME  151 

a  certain  time  of  day  and  on  the  other  it  is  the  same  time  of  either  an 
earlier  or  later  day  according  to  which  side  of  the  line  it  may  be  on. 

When  it  is  9  a.  m.  April  30  at  Honolulu,  long.  157°  20'  W., 
what  is  the  day  and  hour  on  an  island  situated  on  the  equator  in 
the  same  degree  of  longitude  ?  Being  in  the  same  degree  of  longi- 
tude, by  the  ordinary  rule  they  would  have  the  same  day  and 
hour,  but  being  on  different  sides  of  the  date  line  they  differ  in 
time  by  the  equivalent  of  3 GO0  of  longitude,  or  24  hours,  and  as 
the  point  on  the  equator  is  on  the  west  side  of  the  date  line  it 
first  had  April  30,  and  Honolulu  did  not  have  it  for  twenty- 
four  hours  afterward,  hence  it  must  be  9  a.  m.  May  1  at  the 
point  on  the  equator. 

For  such  problems  make  use  of  the  following  rule :  When  the 
date  line  cuts  the  shortest  distance  between  two  places  count  the 
long  way. 

1.  When  it  is  8  p.  m.  Wednesday,  at  Pekin,  long.  116°  east, 
what  is  the  time  at  San  Francisco,  long.  122°  west? 

2.  When  it  is  9  p.  m.  at  San  Francisco,  what  is  the  time  at 
Pekin? 

3.  When  it  is  6  a.  m.  Monday,  at  Salt  Lake  City,  long.  111° 
53'  47"  west,  what  is  the  time  at  Sidney,  long.  151°  11'  east? 

4.  When  it  is  9  p.  m.  at  Omaha,  long.  95°  56'  14"  west,  what 
is  the  time  at  Bombay,  long.  72°  48'  east? 

5.  Com.  Dewey  gave  battle  to  the  Spanish  fleet  in  the  harbor 
of  Manila  at  5  a.  m.  Sunday  morning,  May  1.     If  Manila  is  in 
longitude  120°  E.  and  St.  Louis  is  in  longitude  90°  W.,  what 
hour  and  day  was  it  at  St.  Louis? 

General  Review  Problems 
212.  1.  Reduce  2  mi.  120  rd.  to  feet. 

2.  Reduce  17  T.  5  cwt.  84  Ib.  13  oz.  to  ounces. 

3.  A  farmer  desires  to  send  to  market  58J  bu.  of  wheat  in 
bags  holding  1  bu.  3  pk.  6  qt.    How  many  bags  will  it  require? 

4.  What  will  4  gal.  3  qt.  of  vinegar  cost  at  8c  per  quart? 

5.  5  cents  a  quart  for  sweet  potatoes  is  how  much  per  bushel  ? 

6.  A  boy  picked  14  qt.  of  cherries  a  day  for  15  days.    How 
many  bushels  did  he  pick? 


152  NEW  BUSINESS   ARITHMETIC 

7.  In  286453  grains  apothecaries'  weight  how  many  pounds? 

8.  At  $24.50  per  square  foot,  what  is  a  city  lot  worth  which 
is  38  J  feet  wide  and  102J  feet  long? 

9.  John  Wilson  rented  a  house  for  one  year  for  $420.     He 
occupied  it  from  January  1,  until  November  20,  when  the  house 
was  destroyed  by  fire.     What  rent  did  he  pay? 

10.  How  many  bottles  each  holding  1  pt.  2  gi.  can  be  filled 
from  a  barrel  of  vinegar  ? 

11.  If  a  horse  eats  1  pk.  3  qt.  of  oats  in  a  day,  how  long 
will  16  bu.  3  pk.  3  qt.  last  him? 

12.  Reduce  .185  of  a  day  to  lower  denominations. 

13.  Reduce  .00625  of  a  mi.  to  integers  of  lower  denomina- 
tions. 

IJf-  %  of  a  pwt.  is  what  part  of  a  pound  ? 

15.  What  part  of  5  T.  is  4  cwt.  26  Ibs.  7  oz.  ? 

16.  One  bushel  of  apples  makes  2  gal.  2  qt.  of  cider.     How 
many  gallons  of  cider  can  be  made  from  200  bu.  3  pk.  G  qt.    of 
apples  ? 

17.  When  flour  is  selling  at  $6.75  per  barrel  what  will  a  75 
Ib.  sack  cost  at  the  same  rate  ? 

18.  What  decimal  of  3  days  is  16  hrs.  24  min.  18  sec.? 

19.  What  is  the  difference  between  16f  Ib.  and  13  Ib.  8  oz. 
16  pwt.  15  gr.  ? 

20.  Reduce  9  hrs.  24  min.  18  sec.  to  the  decimal  of  a  day. ' 

21.  Reduce  £  of  a  mile  to  integers  of  lower  denominations. 

22.  What  is  the  value  of  .0725  of  a  ton? 

23.  A  having  a  farm  of  84  A.  136  sq.  rd.  18  sq.  yd.  bought 
at  one  time  24  A.  118  sq.  rd.  26  sq.  yd.  and  at  another  time  116 
A.  32  sq.  rd.  14  sq.  yd.    How  much  land  did  he  then  own  ? 

&4.  Add  f  of  a  mile,  11  f  rods  and  T3c  of  a  rod. 

25.  What  is  the  sum  of  -J  of  a  yard,  -J  of  a  foot  and  -J  of  an 
inch? 

26.  Change  the  difference  between  96  Ib.  13  oz.  and  14  Ib.  15 
oz.  to  the  decimal  of  a  ton. 

27.  What  is  the  cost  of  3  loads  of  apples  each  containing  16 
bu.  3  pk.  5  qt.  at  35c  per  bu.  ? 


LONGITUDE   AND   TIME  153 

28.  What  is  the  cost  of  7  bbl.  of  kerosene  each  containing  44 
gal.  1  qt.  1  pt.  at  12c  per  gal.  ? 

29.  What  is  the  cost  of  1J  A.  land  at  17Jc  per  sq.  ft.? 

50.  George  Washington  was  born  February  22,  1732.     How 
old  was  he  at  the  time  of  the  Declaration  of  Independence  ? 

51.  The  longitude  of  Boston  is  71°  3'  40"  west  and  that  of 
Omaha,  Neb.,  95°  56'  14"  west.     What  is  the  difference  of  time 
between  the  two  places? 

32.  When  it  is  5  min.  past  4  o'clock  a.  m.  at  Sydney,  Aus- 
tralia, what  is  the  time  at  Paris  ? 

S3.  If  a  note  dated  April  6,  1893,  has  2  yr.  3  mo.  23  da.  to 
run,  when  is  it  due? 

34-  How  many  acres  of  land  in  a  field  84  rd.  long  and  38  rd. 
3  yd,,  wide  ? 

35.  How  many  gallons  will  a  cistern  hold  which  is  6  ft.  4  in. 
long,  6  ft.  6  in.  wide  and  10  ft.  8  in.  deep  ? 

36.  How  many  bushels  of  potatoes  will  be  contained  in  a  bin 
16  ft.  8  in.  long,  14  ft.  3  in.  wide  and  9  ft.  6  in.  deep? 

37.  Reduce  84  gal.  to  bushels. 

38.  Reduce  165  bu.  to  gallons. 

39.  Change  24  Ib.  avoirdupois  to  troy  weight. 

40.  Bought  8  bu.  assorted  nuts  at  $4.80  per  bushel  dry  meas- 
ure and  retailed  them  at  30c  a  quart  liquid  measure.    How  much 
was  gained? 


RATIO 

Ratio  is  the  quotient  arising  from  dividing  one  number 
by  another  of  the  same  kind. 

214.  The  Terms  of  a  ratio  are  the  two  numbers  compared. 

215.  The  Antecedent  is  the  first  term  of  a  ratio,  or  dividend. 
The  Consequent  is  the  second  term  of  a  ratio,  or  divisor.     Both 
terms  of  a  ratio  form  a  Couplet. 

216.  The  Symbol  of  a  ratio  is  the  colon  (  :)  which  is  the  sign 
of  division  with  the  line  taken  out;  thus,  8   :  2  is  read:  the  ratio 
of  8  to  2.    Ratio  may  also  be  expressed  in  the  form  of  a  fraction 
by  writing  the  antecedent  for  the  numerator  and  the  consequent 
for  the  denominator,  as  f . 

217.  A  Simple  Ratio  is  a  ratio  that  has  one  antecedent  and 
one  consequent,  as  6  :  4.     The  value  of  the  ratio  is  f  or  1|-. 

218.  A  Compound  Ratio  is  the  product  of  two  or  more  simple 
ratios,  as  (6  :  4)   X  (4  :  2)  ;  the  value  of  the  compound  ratio  is 
f  X  |  or  3. 

From  the  preceding  definitions  we  have  the  following: 

PRINCIPLES  OF  RATIO 

1.  Ratio  =  antecedent  -=-  consequent. 

2.  Antecedent  =  consequent  X  ratio. 

3.  Consequent  =  antecedent  -f-  ratio. 

1.  What  is  the  ratio  of  16  to  8  ? 

SOLUTION  EXPLANATION.— Since  16  is  the  dividend 

-i-o         i  a    .  o   and  8  is  the  divisor  we  find  the  quotient  or 

ID     .  o  =  ID   -7-   o  =  4  ,        ,.    .    . 

ratio  by  division. 
From  the  preceding  we  have  the  following  rule : 

To  Find  a  Ratio 

a.  Divide  the  antecedent  by  the  consequent. 

NOTES. — 1.     Since  the  ratio  may  be  expressed  in  the  form  of  a  fraction, 
the  principles  of  fractions  apply  to  ratio. 

154 


RATIO  155 

2.  Since  only  like  numbers  can  be  compared,  there  can  be  no  ratio 
between  $6  and  8  yd.  or  5  men  and  3  chairs. 

2.  What  is  the  ratio  of  32  to  8  ? 

3.  What  is  the  ratio  of  15  to  36  ? 

4.  What  is  the  ratio  of  16  ft.  8  in.  to  1  ft.  10  in.? 

5.  What  is  the  ratio  of  16  to  82  ? 

6.  What  is  the  ratio  of  }  to  f  ? 

7.  What  is  the  ratio  of  4J  to  11 J? 

8.  What  is  the  ratio  of  5  gal.  3  qt.  to  2  gal.  2  qt.  1  pt.? 

9.  What  is  the  ratio  of  56  bu.  2  pk.  4  qt.  to  4  bu.  2  pk.  7  qt.  ? 

10.  The  antecedent  is  85  and  the  ratio  is  5.    What  is  the  con- 
sequent ? 

11.  The  consequent  is  2.16  and  the  ratio  is  14.5.     What  is 
the  antecedent? 

12.  The  consequent  is  J  and  the  antecedent  is  T\.    What  is  the 
ratio  ? 

IS.  Find  the  compound  ratio  of  J   jj  :  ^  }  . 

( 12  :    3  ) 

14.  What  is  the  difference  between  the  compound  ratios  of 


PROPORTION 

219.  Proportion  is  an  equality  of  ratios  and  is  either  Simple 
or  Compound. 

220.  Simple  Proportion  is  an  equality  of  two  simple  ratios. 

The  symbol  of  proportion  is  the  double  colon  (  :  :)  and  signi- 
fies the  same  as  =,  thus,  18  :  9  :  :  6  :  3  is  read  "18  is  to  9  as  6  is 
to  3." 

221.  The  Terms  of  a  proportion  are  the  four  numbers  com- 
pared. 

222.  The  Extremes  of  a  proportion  are  the  first  and  fourth 
terms.    In  the  above  18  and  3  are  the  extremes. 

223.  The  Means  of  a  proportion  are  the  second  and  third 
terms.    In  the  above  9  and  6  are  the  means. 

224.  The  Couplets  of  the  proportion  are  the  ratios  compared. 
In  the  above  18  and  9  are  the  first  couplet,  6  and  3  the  second 
couplet. 


156  NEW   BUSINESS   ARITHMETIC 

A  proportion  may  be  written,  4  :  2  :  :6  :3;4-T-2  —  6-=-3; 
|  ™  J.  When  written  in  the  fractional  form  the  antecedents  are 
written  above  and  the  consequents  below  the  line.  f  =-  f,  re- 

4X3        6X2 

duced  to  a  common  denominator   •— - —  =  -      — ;    since  numer- 

6  6 

ators  of  similar  fractions  are  to  each  other  as  integral  numbers, 
4  X  3  =  6  X  2,  but  4  and  3  are  the  first  and  last  terms  (ex- 
tremes), 6  and  2  are  the  second  and  third  terms  (means).. 

When  any  three  terms  of  a  proportion  are  given  the  other 
term  may  be  found  by  the  following : 

Principles  of  Proportion 

1.  The  product  of  the  means  equals  the  product  of  the  ex- 
tremes. 

2.  The  product  of  the  means  divided  by  one  extreme  equals 
the  other  extreme. 

S.  The  product  of  the  extremes  divided  by  one  mean  equals 
the  other  mean. 

Find  the  unknown  term  in  the  following: 

1.  6  :  2  :  :  9  :  — .  9.  7£  :  }  :  :  —  :  4. 

2.  10  :  4  :  :  —  :  6.  10.  3J  :  —  :  :  8  :  3. 

3.  9:—  :  :6  :  8.  11.  —  :  J  :  :  6  :  2. 

4.  -  -  :  48  :  :  6  :  8.  12.  $4J  :  $3  :  :  6  Ib.  :  —  Ib. 

5.  $5  :  $12  :  :  10  ft.  :  —  ft.  13.  9  horses  :  15  horses  :  :  - 

6.  $21  :  $7  :  :  —  ft.  :  3  ft.  T  :  5  T. 

7.  15  oz.  :  —  oz.  :  :  8  bu.  :  10  bu.  14.  5i  gal.  :  —  gal.  :  :  $7  :  $8. 

8.  f  :  5  :  :  7  :  — . 

225.  In  any  problem  in  simple  proportion  three  terms  are 
given,  and  a  fourth  term  is  required. 

226.  To  Make  a  Statement  in  proportion  is  to  arrange  the 
three  given  terms,  so  that  two  of  them  form  one  ratio,  the  remain- 
ing term  and  the  unknown  term  another  ratio. 

1.  If  8  barrels  of  potatoes  cost  $20,  what  will  25  barrels  cost? 

SOLUTION 
brl.     brl.  $.         $. 

8  :  25  :  :  20  : — 
25  X  20  -f-  8  =  62J. 


RATIO  157 

Therefore  we  have  the  following  rule : 

To  Find  the  Fourth  Term  of  a  Proportion 

a.  Place  for  the  third  term  that  which  is  of  the  same  denom- 
ination as  required. 

b.  If  the  term  required  be  greater  than  the  third  term,  place 
the  larger  of  the  other  two  numbers   for   the   second    term;    if 
smaller,  place  the  smaller  of  the  two  numbers  for  the  second  term. 

c.  Multiply  the  third  term  by  the  second  and  divide  by  the 
first. 

NOTES. — 1.  If  the  terms  of  any  couplet  be  of  different  denominations, 
they  must  be  reduced  to  the  same  unit  value. 

2.  If  the  divisor  and  dividend  contain  one  or  more  factors  common 
to  both,  they  should  be  cancelled. 

2.  If  15  acres  of  land  produce  535  bu.  of  oats,  how  many 
bushels  will  32  acres  produce  ? 

3.  If  6  barrels  of  flour  cost  $32,  what  will  75  barrels  cost? 

4.  What  must  be  paid  for  15  tons  of  hard  coal,  if  2  tons 
cost  $15  ? 

5.  If  8  men  earn  $75  in  one  week,  how  much  will  14  men 
earn  in  the  same  time  ? 

6.  If  $90,  principal,  produces  $12.60,  how  much  interest  will 
$420  produce? 

7.  I  paid  $42.50  for  17  barrels  of  apples.    How  many  barrels 
could  I  buy  for  $85  ? 

<9.  I  can  walk  12  miles  in  4  hours.  How  many  hours  will  it 
take  to  walk  57  miles  ? 

9.  If  23  trees  bear  143  bu.  3  pk.  of  apples,  how  many  apples 
will  96  trees  bear? 

10.  If  18  barrels  of  flour  contain  3528  lb.,  how  many  pounds 
will  26  bbl.  contain  ? 

11.  What  is  the  cost  of  17  gal.  1  qt.  of  wine,  if  3  gal.  cost 
$4.40? 

12.  I  borrowed  $320  for  3  mo.  18  da.    For  what  time  should 
I  loan  $212  to  return  the  favor  ? 

13.  If  f  of  a  yard  of  cloth  cost  18c,  what  will  7J  yd.  cost? 

14-  25  men  built  a  wall  120  ft.  long  in  a  day.  How  many  feet 
will  65  boys  build  a  day,  if  5  boys  do  as  much  as  4  men  ? 


158  NEW   BUSINESS   ARITHMETIC 

15.  If  15  men  can  build  a  bridge  in  10  days,  how  many  men 
will  be  required  to  erect  three  of  the  same  dimensions  in  J  the 
time? 

16.  If  a  man  receive  $4.50  for  3  days'  work,  how  many  days 
ought  he  to  remain  in  his  place  for  $25  ? 

17.  If  a  troy  ounce  of  gold  is  worth  $19.20,  what  is  an  avoir- 
dupois ounce  worth? 

18.  If  3   cwt.   14  Ibs.  of  sugar  cost  $15.70,  what  will   42 
Ibs.  cost? 

19.  A  butcher  used  a  false  weight  14|  oz.  ,  instead  of  16  oz. 
for  a  pound.    Of  how  many  Ibs.  did  he  defraud  a  customer  who 
bought  112  Ibs.  from  him? 

20.  Suppose  a  certain  pasture,  in  which  are  20  cows,  is  suffi- 
cient to  keep  them  6  weeks  ;  how  many  must  be  turned  out,  that 
the  same  pasture  may  keep  the  rest  24  weeks. 

COMPOUND  PROPORTION 

221.  Compound  Proportion  is  an  equality  of  ratios,  when  one 
or  both  are  compound. 

Any  problem  in  compound  proportion  may  be  stated  and 
solved  as  in  simple  proportion,  and  all  of  the  principles  and  ex- 
planations of  simple  proportion  apply  equally  to  compound  pro- 
portion. 

22S.  Cause  and  Effect  is  a  method  of  stating  problems  in 
Compound  Proportion. 

Cause  and  Effect  is  based  upon  the  principle  that  like  causes 
produce  like  effects,  and  that  effects  are  in  proportion  to  their 
causes. 

1.  If  8  men  will  mow  24  acres  of  grain  in  9  days  of  8  hours 
a  day,  how  many  men  will  be  required  to  mow  48  acres  in  12  days 
working  9  hours  a  day  ? 

EXPLANATION.  —  The  first  cause 
produces  the  first  effect  and  the 

1st  Cause.   2d  Cause.  1st  Effect.  2d  Effect,      second  cause  produces  the   sec- 
8  V  X  ond   effect.     8   men,   9   days,   8 

yf:     \     $$.       hours  constitute  the  cause  which 
3  4         effects  24  acres  to  be  mown.    An 

lOf  .  unknown  number  of  men,  X,  12 

days,    9    hours    constitute    the 


. 

V  X 

\  ^2   :    : 
(     fy 


RATIO  159 

second  cause  which  effects  48  acres  to  be  mown.  The  X  or  unknown 
quantity  may  appear  in  either  of  the  four  terms,  and  should  be  placed 
wherever  the  question  of  the  unknown  appears  in  the  problem.  Employ 
cancellation  between  any  mean  and  any  extreme.  Multiply  the  remaining 
extremes  together  and  divide  by  the  remaining  mean ;  the  result  will  be 
the  unknown  mean. 

From  the  foregoing  solution  and  explanation  we  have  the  fol- 
lowing rule  to  find  the  unknown  quantity  by : 

Cause  and  Effect 

a.  Write  for  the  first  term  the  first  cause  and  its  effect  for  the 
third  term.     Write  for  the  second  term  the  second  cause  and  its 
effect  for  the  fourth  term. 

b.  Place  the   X    in  whichever  cause  or  effect  the  question 
occurs  in  the  problem. 

c.  Cancel  from  either  mean  to  either  extreme,  multiply  the  re- 
maining means  together  and  the  remaining  extremes  together  and 
divide  one  by  the  other.    The  result  will  be  the  unknown  term. 

2.  If  12  horses  eat  18  loads  of  hay  in  8  weeks  how  many 
weeks  will  it  take  20  horses  to  eat  32  loads  of  hay  ? 

3.  If  a  stone  15  ft.  long,  6  ft.  thick,  weighs  12  tons,  how  long 
must  a  stone  be  that  weighs  20  tons,  and  is  5  ft.  thick  ? 

4.  If  the  carpet  for  a  room  24  by  18  ft.  costs  $12,  what  will  it 
cost  to  carpet  a  room  30  by  22  ft.  ? 

5.  I  paid  $1800  for  a  lot  125  by  188  ft.    What  will  a  lot  cost 
whose  dimensions  are  320  by  400  ft.  ? 

6.  If  6  men  in  18  days  of  10  hours  each,  earn  $220,  how  much 
can  9  men  earn  in  24  days  of  9  hours  each  ? 

7.  If  a  box  12  ft.  long,  8  ft.  high  and  6  ft.  wide  contains  480 
bushels,  how  high  is  a  box  15  ft.  long,  5  ft.  wide  that  contains 
500  bushels. 

8.  If  27  hogs,  each  weighing  280  Ibs.,  cost  $960,  what  will  36 
hogs,  each  weighing  350  Ibs.  cost? 

9.  If  $900  for  1  yr.  4  mo.  at  6%  earns  $72  interest,  what  will 
$630  earn  in  2  yr.  1  mo.  at  9%  ? 

10.  What  will  be  the  cost  of  18  logs,  24  ft.  long,  15  in.  wide 
and  9  in.  thick,  if  4  logs,  16  ft.  long,  10  in.  wide  and  8  in.  thick, 
cost  $45  ? 


165  NEW   BUSINESS   ARITHMETIC 

11.  If  120  men  in  9  days  of  8  hours  each,  build  a  wall  80 
rods  long,  6  ft.  high  and  4  ft.  wide,  how  many  hours  per    day 
must  90  men  work  to  build  a  wall  65  rods  long,  5  ft.  high,  4  ft. 
wide  in  12  days? 

12.  What  will  a  pile  of  brick  33  ft.  long,  18  ft.  high  and  15 
ft.  wide  cost  if  a  pile  24  ft.  long,  15  ft.  high  and  11  ft.  wide,  cost 
$325? 

13.  What  will  it  cost  to  paper  the  walls  of  a  room  25  ft.  long, 
18  ft.  wide  and  12  ft.  high,  if  it  cost  $44.20  to  paper  the  walls  of 
a  room  36  ft.  long,  28  ft.  wide  and  10  ft.  high? 

14-  If  12  pieces  of  cloth,  each  containing  34  yd.,  J  yd.  wide, 
cost  $204,  what  will  8  pieces  cost,  each  containing  42  yd.,  f  yd. 
wide  ? 

15.  If  4  men,  working  8  hours  a  day,  can  reap  a  field  of  grain 
of  20  acres  in  8  days,  in  how  many  days  can  9  men,  working  10 
hours  a  day,  reap  a  field  containing  35  acres? 

16.  If  25  men  can  build  a  wall  4800  ft.  long,  7  ft.  high,  and 
1J  ft.  thick  in  42  days  of  8  hours  each,  in  how  many  days  of  10 
hours  each  will  200  men  build  a  similar  wall  1  mile  long,  8  ft. 
high  and  2  ft.  thick? 

'17.  If  the  interest  on  $540  for  1  year  (360  days)  at  5%  in- 
terest is  $27,  what  is  the  interest  on  $925  for  284  days  at  7%  ? 

18.  If  a  person  can  read  a  book  containing  380  pages,  each 
page  containing  42  lines,  each  line  12  words,  in  17^  hours,  how 
many  hours  will  be  required  to  read  2  books,  each  containing  480 
pages,  each  page  50  lines,  and  each  line  15  words? 

19.  If  a  bin  8  ft.  long,  4J  ft.  wide,  and  2J  ft.  deep  holds  67^ 
bu.,  how  deep  must  another  bin  be  made  that  is  24  ft.  long  and 
6J  ft.  wide  to  hold  625  bu.? 

20.  How  many  men  will  be  required  to  excavate  a  cellar  40 
ft.  wide,  172   ft.  long,  and  16  ft.  deep,  in  12  days  of  8  hours 
each,  if  6  men  can  dig  a  similar  one  14  ft.  long,  12J  ft.  wide  and 
8  ft.  deep  in  5  days  of  10 J  hours  each? 

21.  If  4  compositors  in  18  days  of  8  hours  each,  set  up     165 
pages  of  a  book,  each  page  containing  34  lines,  each  line  contain- 
ing 10  words,  and  each  word  containing  on  an  average  8  letters, 
in  how  many  days  of  9J  hours  each,  can  6  compositors  set  up  a 
book  of  340  pages,  each  page  48  lines,  each  line  11  words,  and 
each  word  9  letters  ? 


MEASUREMENTS   USED  IN   BUSINESS 

229.  In  estimating  labor  and  materials,  contractors  use  the 

following : 

TABLE  OF  STANDARD  UNITS 

1  square  foot  =     144  sq.  inches. 

1  square  yard  =         9  sq.  feet. 

1  square  =     100  sq.  feet. 

1  cubic  foot  =  1728  cu.  inches. 

1  cubic  yard  =       27  cu.  feet". 

NOTE. — In  writing  dimensions,  the  accent  mark  (')  is  used  to  indicate 
feet  and  the  double  accent  (")  ;  to  represent  inches.  Thus  4  ft.  3  in.  are 
written  4'  3". 

230.  Excavating  is  estimated  by  the  cubic  yard  of  the  actual 
amount  of  material  displaced. 

A  cubic  yard  of  earth  in  its  natural  position  will  occupy  from 
1J  to  H  cu.  yds.  when  dug. 

On  public  works  a  cu.  yd.  of  earth  is  a  standard  load. 

231.  Foundations  are  estimated  by  the  cubic  foot,  in  either 
concrete  or  stone. 

Foundations  are  generally  composed  of  either  concrete  or 
large  flat  stones,  called  dimension  stones. 

In  estimating  foundations  of  either,  the  concrete,  dimension, 
or  rubble  stone,  the  actual  contents  are  measured. 

"\Yhen  foundations  are  composed  of  rubble  stone  they  are  esti- 
mated by  the  perch  at  24-2  cu.  ft. 

232.  Rubble  Stone  Work. — Stone  is  estimated  by  the  perch. 
All  of  the  outside  walls  of  buildings  below  the  surface  of  the 

ground  are  usually  composed  pf  rough    stone    or    rubble    stone 
work. 

In  estimating  rubble  stone  work  a  perch  of  24f  cu.  ft.  is  used 
11  lei 


162  NEW   BUSINESS   ARITHMETIC 

extensively  by  contractors.  In  the  western  states  the  cord  con- 
sisting of  100  cu.  ft.  is  sometimes  used.  T^  is  allowed  for  mortar. 

In  measuring  for  the  amount  of  stone  or  brick  required  in  a 
building,  girt  the  building  and  subtract  four  times  the  thickness 
of  the  wall  for  the  corners. 

Openings  less  than  4'  0"  are  not  deducted. 

Cut  Stone  Work  is  estimated  by  the  cubic  foot. 

The  stone  used  for  the  facing  and  trimming  of  buildings 
above  the  surface  of  the  ground  is  called  cut  stone,  and  is  esti- 
mated by  the  cubic  foot  for  the  bulk  of  such  material.  This  stone 
is  usually  4"  thick. 

Mouldings,  sills  and  string  courses  are  generally  estimated  by 
the  linear  foot.  * 

233.  Brick  Work  is  estimated  by  the  cubic  foot  and  also  by 
the  thousand. 

Brick  are  of  two  kinds :  Common  and  pressed.  Pressed  brick 
are  used  mostly  for  the  facing  of  walls  of  buildings,  exposed  to 
the  street. 

Pressed  brick  work  is  seldom  more  than  one  brick  or  4"  in 
thickness  and  is  estimated  by  the  superficial  foot. 

Common  brick  of  standard  dimensions  are  8"  x  4"  x  2".  The 
bricks  of  different  localities  may  vary  slightly  from  this. 

7J  bricks  laid  in  a  wall  one  brick  thick  are  usually  estimated 
as  a  square  foot,  and  this  multiplied  by  the  number  of  bricks  in 
the  thickness  will  give  the  number  of  bricks  in  1  sq.  ft.  of  the 
face  of  the  wall. 

In  measuring  for  the  amount  of  material  required,  girt  the 
building  and  subtract  four  times  the  thickness  of  the  wall.  For 
each  corner  of  wall  greater  or  less  than  90°  add  1'  6"  to  length  of 
girt.  Chimneys  and  hollow  walls  are  measured  as  solid.  Circular 
walls  add  J. 

Openings,  if  2'  6"  wide  or  less  are  not  deducted.  Greater  than 
this  deduct  -J. 

234.  Estimating  Work. — In  estimating  the  amount  of  work 
done  in  laying  stone  and  brick,  the  length  of  the  wall  is  found  by 
measuring  around  the  wall  on  the  outside,  or  by  measuring  on  the 


MEASUREMENTS   USED   IN   BUSINESS  163 

inside  and  adding  8  times  the  thickness  of  the  wall.    The  corners 
are  thus  counted  twice  because  more  difficult  to  lay. 

235.  Roofing  is  estimated  either  by  the  square    or    by    the 
thousand  shingles. 

A  shingle  is  estimated  to  average  4"  wide  by  16"  to  18"  long 
and  is  usually  laid  4"  to  the  weather. 

900  shingles  laid  4"  to  the  weather  cover  1  square  of  100  sq. 
ft.  1000  shingles  laid  4"  to  the  weather  will  cover  111  sq.  ft. 
Allowing  for  waste  1000  shingles  are  estimated  to  cover  1  square. 

Slating,  gravel  roofing,  tinning,  etc.,  are  estimated  by  the 
square. 

236.  Concrete  Floors  are  estimated  by  the  superficial  foot  or 
yard. 

No  deductions  are  made  for  piers,  chimneys  or  other  projec- 
tions of  walls  unless  they  amount  to  10  sq.  ft.  in  area. 

237.  Plastering  is  estimated  by  the  square  yard  from  floor  to 
ceiling  for  walls,  and  from  wall  to  wall  for  ceiling. 

Usually  in  measuring  the  plastering  in  a  room,  ^  of  the  open- 
ings are  taken  out.  Plaster  mouldings,  cornices  and  the  like  are 
estimated  by  the  linear  foot.  These  are  measured  on  their  longest 
dimension  and  1'  0"  is  added  for  each  angle  or  corner  around 
which  the  cornice  is  to  break. 

A  bunch  of  lath  contains  50  pieces,  each  4'  long,  and  will 
cover  3'  of  surface. 

Openings  in  lathing  and  plastering  are  not  deducted  unless  2' 
0"  wide.  One-half  of  contents  is  to  be  deducted  for  openings 
from  2'  0"  to  6'  0"  wide. 

238.  Painting  and  Glazing  is  estimated  by  the  square  yard 
or  by  the  square  of  100  sq.  ft. 

In  measuring  a  building  for  painting,  the  tape  is  carried 
around  and  into  all  projections  or  corners. 

In  measuring  doors  take  the  actual  superficial  measurement, 
carrying  the  tape  into  mouldings.  Windows  are  measured  with- 
out allowance  for  glass. 

239.  Carpenter  work  is  estimated  by  the  board  foot. 
Doors  and  windows  are  estimated  by  the  piece. 


164  NEW   BUSINESS   ARITHMETIC 

PROBLEMS 

240.  1.  What  will  be  the  expense  of  excavating  a  cellar  28' 
6"  wide,  42'  3"  long  and  4'  8"  deep  at  $1.30  per  cu.  yard? 

2.  A  cellar  floor  to  be  concreted  is  27'  3"  long  and  13'  8"  widu 
at  8 Jc  per  sq.  foot.    What  will  be  the  cost  ? 

3.  How  many  bricks  8"  x  4"  will  it  take  to  pave  a  yard  which 
is!6'0"x25'0"?' 

4-  The  plans  of  a  house  show  that  it  is  to  contain  five  rooms : 
The  first  12'  0"  x  10'  8",  the  second  15'  0"  x  9'  6",  the  third  14'  0" 
x  9'  10",  the  fourth  11'  3"  x  8'  6",  and  the  fifth  7"  2"  x  5'  9". 
What  amount  of  lumber  will  be  required  to  floor  these  rooms  after 
allowing  J  for  waste  ? 

5.  A  man  having  the  contract  for  excavating  a  cellar  6'  0" 
deep  for  a  house  35'  4"  wide  by  62'  8"  long  at  $1.15  per  cu.  yd. 
finds  on  beginning  the  job  that  the  digging  and  hauling  will  cost 
him  $1.30  per  cu.  yd.  but  he  can  sell  the  dirt  for   $.50   a   yard. 
In  determining  the  amount  of  earth  sold,  assume  that  its  volume 
increases  one-fourth  by  swelling  when  it  is  loosened  in  digging. 
How  much  will  he  make  on  his  contract? 

6.  The  walls  of  a  building  are  V  thick  and  the  building  is 
30'  long  20'  wide  32'  high.     How  many  bricks  of  standard  size 
do  they  contain,  and  what  will  be  the  cost  at  $11  per  M.  bricks? 

7.  Suppose  in  the  preceding  example  the  walls   are   faced 
with  pressed  brick  worth  $40  per  M.  when  laid  in  the  wall,  the 
thickness  of  the  walls  remaining  the  same,  what  are  the  walls 
worth  ? 

8.  Three  piers  of  a  bridge  are  of  rubble  stone  8'  0"  wide,  24' 
0"  long  and  28'  G"  high.     What  will  they  cost  at  40c  per  cubic 
foot,  making  no  allowance  for  excavating? 

9.  How  many  perch  of  stone  are  contained  in  the  walls  of  a 
cellar  30'  0"  wide,  50'  8"  long,  9'  6"  high  and  1'  3"  thick? 

10.  There  are  three  rooms  in  the  basement  of  a  house.     The 
first  is  1G'  0"  x  9'  G";  the  second  is  12'  4"  x  8'  0",  and  the  third  is 
10'  8"  x  8'  6".     What  will  it  cost  to  concrete  the  floors  of  these 
three  rooms  at  8c  per  square  foot  ? 

11.  How  much  will  it  cost  to  plaster  a  room  if  the  length  is 


MEASUREMENTS    USED   IN    BUSINESS  165 

25'  0",  the  width  16'  0",  and  the  height  17'  5"  at  15c  per  square 
yard  ? 

12.  How  many  feet  of  2x4  studding  will  be  required  for  a 
partition  23'  9"  in  length,  10'  0"  high,  if  they  stand  15"   to   cen- 
ters  (one  stud  at  each  end),  making  no  allowance  for  waste? 
What  will  be  the  cost  of  the  studding  at  $17  per  M.  ? 

13.  The  joists  in  a  house  are  16'  long  and  are  2  x  6's  laid  1' 
4"  to  centers  for  a  distance  of  48'  0".     What  will  they  cost  at 
$18  per  M.  ? 

14-  How  many  bricks  are  required  for  a  building,  the  walls 
of  which  are  58'  long,  25'  wide,  44'  high,  and  1'  thick,  making 
no  allowance  for  windows,  doors,  or  corners. 

15.  At  $3.75  per  M.  for  bricks,  and  $4.25  per  M.  for  laying 
them,  what  will  the  walls  of  such  a  building  cost? 

1<>.  I  wish  to  saw  a  square  yard  from  a  plank  .15"  wide  and 
2"  thick.  How  far  from  the  end  must  I  cut  ? 

17.  What  is  the  difference  in  area  between  2  rectangles,  the 
first  being  4'  5"  x  (>'  8"  and  the  second  5'  4"  x  8'  6". 

18.  How  many  ordinary  bricks  required  for  the  walls  of    a 
house,  60'  deep,  36'  high,  24'  wide,  if  240  sq.    feet   be    allowed 
for  windows  and  doors,  the  walls  being  3«bricks  thick? 

19.  In  the  walls  of  a  cellar,  the  thickness  of  which  is  1'  6", 
the  height  8',  each  side  wall  52'  and    each    end    wall    25'    how 
many  perch  of  stone  ?    At  $4.87 J  a  perch,  what  will  it  cost  to  build 
the  walls  of  this  cellar  ? 

20.  What  will  it  cost  to  wainscot  both  sides  of  a  hall  48'  9" 
long,  to  the  height  of  5'  at  75c  per  sq.  ft.  ? 

21.  A  skylight  is  42'  long  and  the  rafters  are  16'  4"  long  on 
each  side  to  the  ridge.    What  will  be  the  cost  of  glazing  the  same 
at  60c  per  square  foot,  the  gables  not  being  glazed? 

22.  What  will  be  the  cost  of  a  gravel  roof  on  a  building  50' 
x  150',  deducting  for  a  court  25'  x  40',  at  $3.50  per  square? 

23.  It  is  desired  to  shingle  a  roof:  the  following  dimensions 
are  given :   Length  100  ft.,  width  24  ft. ;  shingles  to  be  exposed 
4  inches  and  average  4  in.  in  width,  the  shingles  on  the  lower 
course  being  doubled.     The  shingles  will  cost  $3.25  per  M.  and 


166  NEW   BUSINESS   ARITHMETIC 

it  will  cost  $2  per  M.  to  lay  them.    What  will  it  cost  to  put  on 
the  roof? 

@4-  The  roof  of  a  barn  is  50  ft.  long,  and  the  width  of  each 
side  is  25  ft.  from  the  ridge  to  the  eaves.  Shingles  are  to  be  laid 
exposed  5  in.  to  the  weather  and  average  4  in.  in  width.  If  the 
first  course  is  doubled  on  each  side,  how  many  shingles  will  be 
required  for  the  roof? 


PERCENTAGE 

241.  Percentage  is  the  department  of  arithmetic,  which 
treats  of  all  operations  in  which  100  is  the  basis  of  computation. 

24:2.  The  term  Per  Cent,  from  the  Latin,  per  centum,  means 
by,  or  on  the  hundred.  2  per  cent,  is  2  of  every  hundred  or  two 
hundredths.  $3  gain  on  $100  is  a  gain  of  3  per  cent,  or  three 
hundredths  on  each  dollar. 

243.  The  Sign  %  is  generally  used  for  the  words  per  cent.; 
4%  means  4  per  cent.,  8J%  means  8-J  per  cent. 

244.  Since  any  Per  Cent,  is  a  number  of  hundredths,  it  may 
be  written  as  a  decimal  or  a  fraction.    Thus  6  per  cent.  =  6%  = 
.06  =  jib. 

Since  hundredths  occupy  two  places,  every  per  cent,  requires  at  least 
two  decimal  figures,  and  if  the  per  cent,  is  less  than  10  a  cipher  must  be 
prefixed  to  the  figure  denoting  the  per  cent. 

When  the  decimal  point  is  used  in  expressing  any  per  cent.,  the  words 
per  cent,  and  the  sign  %  are  omitted ;  when  the  words  per  cent,  or  the  sign 
%  is  used,  the  decimal  point  is  omitted. 

245.  In  solving  problems  in  Percentage,  five  quantities  are 
considered:    Base,  Rate,  Percentage,  Amount  and  Difference. 

246.  The  Base  is  that  on  which  Percentage  is  computed. 

247.  The  Rate  is  the  number  of  hundredths  to  be  taken   of 
each  unit  of  the  Base. 

248.  The  Percentage  is  the  number  of  hundredths    of    the 
whole  Base  as  indicated  by  the  Rate. 

249.  The  Amount  is  the  sum  of  the  Base  and  the  Percentage. 

250.  The  Difference  is  the  difference  between  the  Base  and 
the  Percentage. 

In  all  departments  of  Arithmetic,  except  Percentage,  we  use  one  as 
the  basis  of  computation,  while  in  Percentage,  we  use  one  hundred  as  the 
basis  of  computation ;  in  this  only  does  the  work  differ. 

The  principal  applications  of  Percentage  are  to  the  computa- 
tion of  Commission,  Brokerage,  Insurance,  Profit  and  Loss, 
Duties  or  Customs,  Interest,  Discount  and  Exchange. 

167 


168  NEW    BUSINESS   ARITHMETIC 

In  Percentage  and  all  its  applications 

1.  The  Base  is  represented  by  100%. 

2.  The  Amount  is  represented  by  100%  plus  the  given  rate. 

3.  The  Difference  is  represented  by  100%  minus  the  given 
rate. 

4'  The  Percentage  is  represented  b\  the  given  Rate. 
251.  Given  Base  and  Rate  to  find  Percentage. 

ORAL  PROBLEMS 

1.  If  100%  =  the  whole  of  a  thing,  what  part  of  it  is  50%  ? 
25%  ?  20%  ?  10%  ?  5%  ?  4%  ?  2%  ? 

2.  How  would  you  get  50%  of  a  thing?  2S%  ?  20%? 
S.  What  is  25%  of  a  bushel  of  apples?  50%?  75%? 
4*  What  is  25%  of  4  bushels  of  apples?  50%?  75%? 

5.  What  is  33^%  of  6  bu.?  12  bu.?  24  bu.?  75  bu.? 

6.  What  is  50%  of  18  qt.  ?  37  qt.  ?  45  qt.  ?  63  qt.  ? 

7.  What  part  of  a  thing  is  121'%  ?  37-J%  ?  62J%  ?  87J%  ? 

8.  What  is  37  J%  of  $40?  $56?  $64?  $72?  $88?  $96? 

9.  A  man  has  $120  and  lost  12J%  of  it,  how  much  did  he 
lose,  and  how  much  has  he  left? 

10.  A  mzn  having  $150  spent  10%  for  board,  20%  for  a  suit 
of  clothes  and  5%  for  books.  How  much  did  he  spend  for  each 
and  how  much  has  he  left? 

WRITTEN   PROBLEMS 

1.  What  is  20%  of  $840? 

SOLUTION  Or 

1.  100%  =  $840.  $840  Base. 

2.  1%  ==  $8.40.  _^o  Rate. 

3.  20%  =  $168.  $168X)0~  Percentage. 

From  this  solution  and  explanation  we  have  the  following 
method  of  solution : 

To  Find  the  Percentage 

a.  Let  100%  equal  the  given  number  or  Base. 

b.  Find  the  value  of  1%  by  pointing  off  two  decimal  places. 

c.  Find  the  value  of  the  given  Rate  by  multiplication. 
Or,     Multiply  the  Base  by  the  Rate  expressed  decimally. 


PERCENTAGE  169 

2.  What  is  6%  of  $400? 
s     3.  What  is  12%  of  $950? 

4.  What  is  18%  of  $1-440? 

5.  What  is  24%  of  $2160? 

6.  What  is  35%  of  $1750? 

7.  What  is  45%  of  1800  bushels? 

8.  What  is  52%  of  20500  men? 

9.  What  is  115%  of  3462  feet? 
10.  What  is  165%  of  2450  pounds? 

/  11.  Whatis8f%  of  $480? 

J£.  What  is  6|%  of  24360  bushels? 
,     13.  What  is  14%  of  J? 

14.  What  is  2i%  of  7J? 

15.  What  is  33  J%  of  TV 

16.  What  is  |%  of  $28.30? 

17.  What  is  J%  of  $420? 

18.  A  man  had  $2460  and  gained  in  business  28%    of    this 
amount.    What  was  his  gain  ? 

19.  A  merchant  having  $5640  worth  of  goods  in  store,    re- 
duced his  stock  25%  by  an  auction  sale.    What  amount  of  goods 
was  sold,  and  what  amount  still  remained? 

20.  Bought  a  house  and  lot  for  $6450  and  sold  it  for  92%  of 
its  cost.    What  was  the  loss? 

21.  What  is  the  difference  between  19%  of  $2635,  and  15% 
of  $3267? 

22.  A  library  was  sold  for  $4500.     A  bought  30%  of  it;  B 
25%  ;  C  20%,  and  D  the  remainder.    What  per  cent,  of  the  whole 
was  D's  purchase  and  what  did  it  cost  him  ? 

28.  A  banker  failed  but  afterwards  paid  34%  of  his  indebted- 
ness. He  owed  Jones  $2475  and  Brown  $1432.  How  much  will 
each  receive  ? 

24.  A  man  owning  J  of  a  store  building  sold  60%  of  his  share. 
What  part  of  the  building  did  he  sell  and  what  part  did  he  still 


own 


25.  Find  10%  of  20%  of  $265. 

26.  Find  40%  of  20%  of  15%  of  $450. 


170  NEW   BUSINESS   ARITHMETIC 

27.  A  owed  B  a  sum  of  money.     At  one  time  he  paid  him 
4:0%  of  it;  at  another  time  he  paid  25%  of  what  was  still  owing. 
How  much  then  remained  unpaid? 

28.  A  grain  dealer  bought  16240  bushels  of  grain,  of  which 
36%  was  wheat,  27%  was  oats,  18%  was  rye  and  the  balance 
was  corn.    How  many  bushels  of  corn  did  he  buy  ? 

29.  A   newspaper   publisher   having    4560     subscribers,    lost 
12%%  of  them;  20%  of  the  remainder  failed  to  pay.    How  many 
paying  subscribers  had  he  ? 

30.  I  had  $1600  deposited  in  a  bank.    On  July  1st  I  drew  out 
20%  of  it;  on  August  15,  16f%  of  the  remainder  and  on  Septem- 
ber 10;  an  amount  equal  to  75%  of  the  amounts  previously  drawn. 
How  much  still  remained  in  the  bank  ? 

252.  When  the  given  per  cent,  is  an  aliquot  part  of  100,  in- 
stead of  multiplying  by  the  rate,  multiply  by  the  aliquot  part  of 
100.    Thus: 

2$%  =  A-          m%  =  i         33J%  =  J. 

5%     =  ^         16f  %  =  J.         50%  .  =  1. 

8$%  =  TV         20%     ==  i.         66f%  =  f. 

10%     =  TV.         25%     =  1.         75%     =  J. 

Find  the  percentage  in  the  following  problems : 

1.  20%  of  $560.  7.  10%  of  286  doz. 

2.  25%  of  1280  bu.  8.  12$%  of  1432. 

3.  33J%  of  3645  yd.  9.  2$%  of  $3600. 

4.  16f  %  of  1428  Ib.  10.  50%  of  2436. 

5.  6i%  of  $2860.  11.  8J%  of  168  bbl. 

6.  5%  of  4532  yd.  12.  25%  of  $1472. 

253.  Given  Base  and  Rate  to  find  Amount  or  Difference. 

ORAL  PROBLEMS 

i          1.  What  is  25%  more  than  a  whole  thing?  50%  ?  37£%  ? 

2.  What  is  $40  plus  25%  of  itself?  20%  ?  50%  ?  75%  ? 

3.  What  is  60  bu.  less  10%  of  itself?  20%  ?  25%  ?  75%  ? 

4.  A  has  $100,  he  spends  20%  for  a  fishing  outfit,  10%  of  the 
remainder  for  a  pair  of  shoes  and  75%  of  the  remainder  for  rail- 
road fare.    How  much  did  he  spend  for  each  and  how  much  has 
he  left? 


PERCENTAGE  171 

5.  A  merchant  starts  in  business  with  $500;  the  first  year  he 
increased  his  capital  20%  and  the  second  year  he  increased  this 
sum  25%.  How  much  had  he  at  the  end  of  the  second  year? 

WRITTEN  PROBLEMS 

1.  A  man  bought  a  horse  for  $108,  and  sold  it  for  25%  more 
than  the  cost.  What  did  he  receive  for  the  horse  ? 

SOLUTION 

1.  100%   +  25%  =  125%,  the  amount. 

2.  100%  =  $108. 

3.  l%  =  $1.08. 

4.  125%  =  $135. 


$135.00 

From  the  foregoing  solution  we  have  the  following: 
To  Find  the  Amount  or  Difference 

a.  Add  the  given  Rate  to  100%  if  the  Amount  is  required,  or 
subtract  the  given  Rate  from  100%  if  the  Difference  is  required. 

b.  Let  100%  equal  the  given  number  or  Base. 

c.  Find  the  value  of  1%  by  pointing  off. 

d.  Find  the  value  of  the  Amount  or  Difference  per  cent,  by 
multiplication. 

Or,  Multiply  the  Base  by  the  Amount  or  Difference  per  cent, 
expressed  decimally. 

2.  The  Base  is  $240,  the  Rate  is  35%,  find  the  Amount. 

3.  The  Base  is  $7.20,  the  Rate  is  20%,  find  the  Difference. 

4.  The  Base  is  130  gals.,  the  Rate  is  40%,  find  the  Amount. 

5.  The  Base  is  225  feet,  the  Rate  is  33J%,  find  the  Differ- 
ence. 

6.  The  Base  is  2500  yds.,  the  Rate  is  12 J%,  find  the  Amount. 

7.  What  is  received  for  a  lot  that  cost  $450,  and  is  sold  for 
20%  less  than  cost? 

8.  A  man  invested  $4850  and  gained  22%  during  the  year. 
How  much  was  his  capital  at  closing  ? 

9.  A  dealer  bought  26  hogs  at  $5.50  each,  and  sold  them  at  a 


172  NEW   BUSINESS   ARITHMETIC 

gain  of  18%.    What  did  he  receive  for  them?    If  he  had  sold  at 
a  loss  of  26%,  what  would  he  have  received? 

10.  A  field  produced  last  year  405  bushels  of  wheat.     It  pro- 
duced 65%  more  this  year.     How  many  bushels  did  it  produce 
this  year  ? 

11.  I  bought  400  sheep  and  lost  10%  of  them,  after  which  I 
sold  45%  of  what  I  had  left.    How  many  did  I  have  left? 

12.  A  hatter  bought  a  hat  for  $5  and  sold  it  so  as  to  gain 
25%.    What  did  the  hat  sell  for? 

IS.  A  speculator  having  $4273,  lost  10%  of  his  money  by  a 
venture.    How  much  did  he  lose,  and  how  much  had  he  left? 

14.  A  merchant  lost  12J%  of  his  sales  by  bad  debts.     His 
sales  amounted  to  $5428 ;  what  was  the  amount  of  his  collections  ? 

15.  In  a  school  20%  of  the  pupils  are  absent  and  there  are 
685  enrolled.    How  many  pupils  are  present  in  the  school  ? 

16.  A  merchant  invested  in  business  $12500.     The  first  year 
he  increase^  his  capital  18%,  the  second  year  he  increased  the 
capital  at  the  close  of  the  first  year  24%.     What  was  he  worth 
at  the  end  of  the  second'  year  ? 

17.  A  stock  of  goods  which  cost  $6820,  decreased  in    value 
33-J%  and  then  again  20%  of  its  lessened  value  when  it  was  sold. 
What  did  it  bring  ? 

18.  A  man  dying  left  an  estate  worth  $45000.    He  gave  30% 
of  it  to  his  wife;  20%  of  the  remainder  to  his  elder  son;  25%  of 
the  remainder  to  his  younger  son,  and  the  remainder  to  his  daugh- 
ter.   What  was  the  share  of  each  ? 

19.  A  firm  began  business  with  a  capital  of  $27800.    The  first 
year  they  gained  12%  which  was  added  to  the  capital ;  the  second 
year  they  gained  18%  which  was  added  to  the  capital;  the  third 
year  they  lost  15%.    What  was  the  firm  worth  at  the  end  of  the 
third  year  ? 

20.  A  watch  cost  $134,  and  another  cost  25%  more  than  the 
first.    What  was  the  cost  of  both  ? 

254.  Given  Rate  and  Percentage  to  find  Base. 


PERCENTAGE  17B 

ORAL  PROBLEMS 

1.  25  is  \  of  what  number?  J?  i?  J? 

2.  36  is  i  of  what  number?  i?  J?  f?  f? 

3.  50%  of  a  thing  is  what  part  of  it?  25%  ?  66f  %  ?  75%  ? 

4.  48  is  50%  of  what  number?  75%  ?  66f  %  ? 

5.  One  boy  has  $2.50;  this  is  25%  of  another  boy's  money. 
How  many  dollars  has  this  boy  ? 

0.  $25  is  10%  of  what  number?  20%  ?  30%  ?  40%  ?  50%  ? 

7.  10%  of  $75  is  -J  of  what  number?    i  ?    J  ? 

8.  25%  of  48  bu.  is  50%  of  how  many  bushels? 

9.  37J%  of  72  quarts  is  33J%  of  how  many  quarts? 

10.  33-J-%  of  A's  money  equals  37J%  of  B's  money.     How 
much  money  has  B  if  A  has  $72  ? 

WRITTEN  PROBLEMS 

1.  $840  is  20%  of  what  sum? 

SOLUTION 

1.  20%  of  the  required  sun,  ==  $840. 
'°  =  $ 


$4200 
3.  100%  (the  required  sum)  =$4200. 

From  the  foregoing-  solution  and  explanation  we  have  the  fol- 

lowing : 

Rate  and  Percentage  Being  Given  to  Find  the  Base 

a.  Let  the  given  Rate  equal  the  Percentage  or  number  given. 

b.  Find  the  value  of  1%  by  dividing. 

c.  Find  the  value  of  100%. 

Or,  Divide  the  Percentage  by  the  Rate  expressed  decimally. 

2.  420  is  8%  of  what  number? 

3.  252  is  18%  of  what  number? 

4.  720  is  32%  of  what  number? 

5.  75  is  40%  of  what  number? 

6.  Of  what  sum  of  money  is  $987,  47%  ? 

7.  Of  what  number  of  dollars  is  $45,  2£%  ? 

S.  I  paid  $150  for  a  horse,  and  found  it  had  cost  me 
of  mv  monev.    How  much  had  I  at  first? 


174  NEW   BUSINESS   ARITHMETIC 

9.  A  farmer  sold  90  sheep  which  was  22%%  of  his  flock. 
How  many  sheep  did  he  have  at  first  and  how  many  left? 

10.  A  retail  merchant  bought  from  a  jobber  225  yards  of 
cloth,  which  was  37J%  of  all  the  jobber  had.     How  much  had 
he  before  he  sold  this  ? 

11.  By  selling-  a  house  for  $288  more  than  it  cost,  the  owner 
gained  8%.  What  was  the  cost  and  selling  price  of  the  house? 

12.  Jones  has  $280  which  is  35%  of  Smith's  money  and  9J% 
of  Brown's  money.     How  much  has  each? 

13.  A  farmer  paid  $62.40  for  a  wagon.    The  cost  of  the  wagon 
was  80%  of  the  cost  of  his  horse.     How  much  did  he  pay  for 
both? 

14-  A  field  produced  1470  bushels  of  oats  last  year  and  this 
was  4:2%  of  what  it  produced  this  year.  This  year's  crop  was 
sold  for  34  cents  per  bushel.  Find  the  amount  received. 

15.  A  collector  collected  $2925,  which  was  75%  of  the  claim. 
What  was  the  claim  and  what  was  the  collector's  commission  if 
he  received  3J%  on  the  amount  collected? 

16.  The  assets  of  a  firm  consist  of  cash  $3250,  notes  $1870, 
and  real  estate  $2740.     The  assets  are  39-^%  of  the  liabilities. 
What  are  the  liabilities  of  the  firm  ? 

17.  The  expenses  of  a  clerk  are  as  follows:    $180  for  board, 
$72  for  lodging,  $68  for  clothes,  $25  for  books,  $37  for  incidentals. 
His  total  expenses  are  32%  of  his  salary.    What  is  his  salary? 

18.  A  man  bought  66f%  of  a  flock  of  240  sheep ;  the  number 
he  bought  was  53 \%  of  what  he  already  had.     How  many  sheep 
did  he  buy,  and  how  many  did  he  then  have? 

19.  A  boy  bought  a  pair  of  boots  for  $2.80,  a  cap  for  $.65,  a 
knife  for  $.45,  and  a  pair  of  skates  for  $1.60;  he  had  45%  of  his 
money  left.     How  much  had  he  at  first,  and  how  much  did  he 
have  remaining? 

20.  Brown  gave  his  son  $37.50,  which  was  60%  of  what  he 
gave  his  daughter  and  25%  of  what  he  gave  his  wife;  he  had 
87 \%  of  his  money  left.    How  much  had  he  at  first,  how  much 
did  he  give  his  wife  and  how  much  did  he  give  his  daughter? 

255.  Given  Amount  or  Difference  and  Rate  to  Find  Base. 


PERCENTAGE  175 

ORAL  PROBLEMS 

1.  What  number  plus  25%  of  itself  equals  30? 

2.  What  number  plus  33J%  of  itself  equals  50? 

3.  What  number  minus  25%  of  itself  equals  75? 

4.  What  number  minus  66f  %  of  itself  equals  $45  ? 

5.  What  number  increased  by  25%  of  itself  equals  $25?    45 
bu.?  60  qt?  $120?  2400  min.? 

6.  What  number  diminished  by  12%%  of  itself  equals  21  bu.  ? 
42  hr.?    84  sec.?    $140?    $91? 

7.  A  man  spent  12%  of  his  money,  he  then  finds  that  he  has 
$176.    How  much  had  he  at  first? 

8.  A  has  a  certain  number  of  horses,  he  buys  25%  of  his  pres- 
ent number.    He  now  has  250  horses.    How  many  had  he  at  first ? 

WRITTEN   PROBLEMS 

1.  I  gained  20%  by  selling  my  house  for  $840.     How  much 
did  the  house  cost  me  ? 

SOLUTION 

1.  100%   +  20%  =  120%,  the  amount.  Or, 

2.  120%  =  $840.  1.20)  $840.00 

3.  1%  =  $7.  $700 

4.  100%  =  $700. 

From  the  foregoing  solution  and  explanation  we  have  the  fol- 
lowing : 

Amount  or  Difference  and  Rate  Being  Given,  to  Find  the  Base 

a.  Let  100%  plus  the  given  Rate  equal  the  Amount,  or  100% 
minus  the  given  Rate  equal  the  Difference.  p_ 

b.  Find  the  value  of  1%.  '   l-t  3. 

c.  Find  the  value  of  100%.  ^  -_  jC-^ 
Or,  Divide  the  Amount  or  Difference  by  the  Amount  or  Differ- 
ence per  cent,  expressed  decimal! y. 

2.  $560  is  12%  more  than  what  sum? 

3.  375  is  25%  more  than  what  number? 
4-  280  is  40%  more  than  what  number? 
o.  $440  is  12%  less  than  what  sum? 


176  NEW    BUSINESS   ARITHMETIC 


6.  A's  fence  is  4029  feet  long  which  is  18£%  longer  than  B's. 
How  long  is  B's  fence? 

7.  Smith  raised  2535  bushels  of  corn.     Smith  had  15£%  less 
than  Brown.    How  many  bushels  did  Brown  have? 

8.  A  man  owes  $960  which  is  40%  less  than  the  money  he 
has  on  hand.    How  much  has  he? 

9.  The  weight  of  two  hogs  is  591  pounds,  which  is  1^%  ^ess 
than  the  weight  of  three  others.    Find  the  weight  of  the  five  hogs. 

10.  A  blacksmith  sold  a  wagon  for  $270  and  gained  20%  on 
the  cost.    Find  the  cost  and  what  he  should  sell  for  to  gain  18§%  . 

11.  The  amount  of  a  note  that  was  on  interest  at  8%  for  one 
year,  was  $756.     How  much  was  the  principal,  and  how  much 
was  the  interest? 

12.  I  sold  5%  of  my  sheep  to  A,  4£%  of  them  to  B,  3%  of 
them  to  C.     I  then  had  175  sheep.     Find  the  number  I  had  at 
first  and  the  number  sold  to  each. 

(13.  A  salesman's  salary  is  $726,  which  is  21%  more  than  his 
•salary  for  last  year,  and  that  was  20%  more  than  his  salary  for 
the  previous  year.  Find  his  salary  for  each  year. 

14-  A  house  is  valued  at  $1620,  caused  from  a  rise  of  35%  in 
real  estate,  and  its  value  before  the  rise  was  20%  more  than  its 
first  cost.  Find  the  cost. 

15.  A  farmer  sold  one  horse  for  $175  and  thereby  lost  25%. 
Had  he  sold  the  horse  for  $215  would  he  have  gained  or  lost  and 
how  much? 

1G.  A  man  dying  left  25%  of  his  property  to  his  wife,  50% 
of  the  remainder  to  his  son,  75%  of  the  remainder  to  his  daughter, 
and  the  balance  $500  to  a  servant.  What  was  the  value  of  his 
estate  ? 

17.  1642  is  6%  of  50%  of  87^%  more  than  what  number? 

18.  In  a  company  of  87  the  children  are  37J%  of  the  women, 
who  are  44i%  of  the  men.    How  many  of  each? 

19.  A  dry  goods  merchant  increased  his  sales  20%  the  sec- 
ond year  over  the  first;  30%  the  third  year  over  the  second,  and 

the  fourth  year  over  the  third.     He  then  found  that  his 


PERCENTAGE  177 

total  sales  for  the  first  four  years  had  been  $45552.     What  were 
his  sales  for  the  first  year? 

256.  Given  Base  and  Percentage  to  find  Rate. 

ORAL  PROBLEMS 

1.  15  is  what  part  of  30?  of  45?  of  75?  of  105? 

2.  15  is  what  per  cent,  of  30?  of  45?  of  75?  of  105? 

3.  25  is  what  per  cent,  of  25?    50?   100?  7500? 

4.  1  hr.  20  min,  is  what  per  cent,  of  4  hrs.  ? 

5.  What  per  cent,  of  75  is  15?  25?  50?  150?  225? 

6.  A  has  $50  and  B  has  $75.    A's  money  is  what  per  cent,  of 
B's  money?     B's  money  is  what  per  cent,  of  A's  money?     A's 
money  is  what  per  cent,  of  what  both  have?    B's  money  is  what 
per  cent,  of  what  both  have  ? 

WRITTEN   PROBLEM^ 

1.  A  house  cost  $960  and  was  sold  at  a  profit  of  $240.    What 
per  cent,  of  profit  was  this  ? 

SOLUTION  Or, 

1.  $960  =  100%.  $960) $240.00 (.25  or  25% 

2-       $1  =  &%.  1920 

3.  $240  =  25%.  4800 

4800 

From  the  foregoing  solution  and  explanation  we  have  the  fol- 
lowing : 

Base  and  Percentage  Being  Given  to  Find  the  Rate 

a.  The  Base  equals  100%. 

b.  Find  the  value  of  a  unit  of  the  Base. 

c.  Find  the  value  of  the  Percentage. 

Or,  Divide  the  Percentage  by  1%  of  the  Base. 
2.  18  is  what  %  of  360  ? 
5.  $48  are  what  %  of  $400? 

4.  35  sheep  are  what  %  of  500  sheep? 

5.  75  yards  are  what  %  of  300  yards? 

6.  448  bushels  are  what  %  of  1120  bushels? 

7.  250  Ibs.  are  what  %  of  750  Ibs.  ? 

12 


178  NEW   BUSINESS   ARITHMETIC 

8.  115  feet  are  what  per  cent,  of  920  feet? 

9.  72  gallons  are  what  %  of  864  gallons? 

10.  2  bushels  2  pecks  are  what  %  of  10  bushels? 

11.  A  dealer  bought  a  wagon  for  $72  and  sold  it  for  $21.60 
more  than  it  cost.    What  %  did  he  gain? 

12.  A  farmer  sold  36  bushels  from  a  bin  containing  160  bush- 
els of  oats.    What  %  of  the  oats  did  he  sell  ? 

13.  The  rent  of  a  house  worth  $3600,  is  $720.     The  rent  is 
what  %  of  its  value? 

14'  A  farmer  harvested  420  bushels  of  wheat  from  21  bushels 
of  seed.    The  seed  was  what  %  of  the  amount  harvested  ? 

15.  $768  profit  was  received  from  an  investment  of  $4800. 
Find  the  rate  of  profit. 

16.  Jones  paid  his  attorney  $32.50  for  collecting  a  debt  of 
$520.    What  per  cent,  of  the  debt  was  paid  for  collecting  it? 

17.  A  banker's  assets  are  $4260,  and  his  liabilities  $7100. 
What  %  can  he  pay  his  creditors?    How  much  will  A  receive, 
whose  account  is  $860? 

18.  I  received  $1904  for  a  farm  that  cost  $1700.    How  much 
%  did  I  gain,  and  what  %  would  I  have  lost  by  selling  for  $1445  ? 

19.  A  father  divided  his  estate  of  $2540  among  his  three 
sons:  to  the  oldest,  he  gave  $1016;  to  the  next  oldest,  he  gave 
$889 ;  to  the  youngest  he  gave  $635.    What  %  of  the  estate  did  he 
give  each? 

20.  A  farmer  who  had  650  sheep,  sold  182  to  West;  169  to 
Packard ;  156  to  Young.    What  %  of  the  flock  did  he  retain  and 
what  %  did  each  buy  ? 

21.  A  merchant  bought  an  invoice  of  goods  for  $365.60  and 
sold  them  for  $406.73.    The  gain  is  what  %  of  the  cost? 

22.  A  capitalist  owns  a  house  worth  $7500,  the  income  from 
which  is  $540  a  year.    What  %  does  his  investment  bring  him  ? 

23.  A  Wyoming  cattle  dealer  lost  137  head  of  cattle  during  a 
blizzard  out  of  a  herd  of  548  head.    What  per  ce.nt.  of  the  herd 
was  left? 

24.  A  man  owned  i  interest  in  a  mill  and  sold  25%  of  his 
interest  for  $2860.    His  income  from  remainder  was  $858.    What 
was  the  entire  income  from  the  mill  and  what  %  does  the  mill 
pay? 


PERCENTAGE  179 

REVIEW  PROBLEMS 

257.  1.  Jones  had  275  horses  and  lost  24%  of  them.    What 
number  did  he  lose? 

2.  A  bought  a  drove  of  hogs  for  $2895,  and  sold  them  at 
a  profit  of  8$%.    Find  his  gain; 

3.  How  much  above  cost  must  goods,  that  cost  $9.80  per 
yard,  be  marked  to  gain  15%? 

4.  The  invoice  price  of  a  lot  of  merchandise  was  $710.    A 
discount  of  19%  was  allowed.    Find  the  amount  of  discount. 

5.  I  sold  92  bbls.  of  flour  at  $8.25  per  bbl,  and  received  3J% 
for  selling  same.    What  amount  did  I  receive  ? 

6.  Lyman  sold  90  shares  of  bank  stock  of  $100  each  at  a 
premium  of  llf  %.    How  much  was  the  premium? 

7.  A  farmer  harvested  780  bushels  of  oats  last  year,  and  35% 
more  this  year.    Find  the  number  of  bushels  harvested  this  year. 

8.  Davis  invested  $4368  in  business  and  gained  26J%  on  the 
investment.     Find  his  present  capital. 

9.  Find  the  selling  price  of  cloth  that  cost  $1.46  per  yard,  and 
sold  at  a  gain  of  45%. 

10.  West  purchased  goods  that  were  marked  $18.40,  at  a  dis- 
count of  19  J%.    How  much  did  he  pay  for  the  goods? 

11.  An  agent  purchased  1240  yards  of  cloth  at  95  cents  per 
yard.    He  charged  4J%  for  buying.    How  much  did  he  receive  ? 

12.  B  bought  $6400  worth  of  stock  at  a  discount  of  14%. 
Find  what  the  stock  cost  him. 

13.  A  farmer  bought  72f  acres  of  land,  which  was  16%  of 
what  he  already  had.     Find  the  number  of  acres  he  had  before 
buying. 

14-  A  manufacturer  sold  a  carriage  for  $246.50,  thereby  gain- 
ing 25%.     Find  the  cost  of  the  carriage.* 

15.  Goods  costing  $76,  were  sold  at  12J%  gain.     What  was 
received  for  them,  and  what  would  have  been  received  by  selling 
them  at  6J%  loss? 

16.  Goods  were  sold  at  $384,  at  a  loss  of  14|%.    What  was 
the  cost,  and  what  %  would  have  been  gained  by  selling  them 
for  $492.80  ? 


180  NEW   BUSINESS   ARITHMETIC 

17.  An  agent's  charges  for  buying  were  $22.50  and  his  rate 
of  charges  was  4J%.    What  was  the  amount  of  the  purchase? 

18.  The  dividend  on  stock  was  $837,  the  rate  of  dividend  was 
9%.     Find  the  value  of  the  stock  and  the  number  of  shares  at 
$-100  each. 

19.  B  had  $620.    He  paid  $24  for  a  desk,  $122  for  a  safe,  and 
$71  for  books.    What  %  of  his  money  did  he  pay  out,  and  what 
%  remained? 

20.  The  invoice  price  of  goods  was  $288.     The  discount  al- 
lowed by  the  seller  was  $43.20.    Find  the  rate  of  discount. 

21.  A  horse  dealer  sold  two  teams  for  $240  each.    On  one,  he 
gained  20%  ;  on  the  other,  he  lost  20%.    Did  he  gain  or  lose  by 
the  transaction,  and  how  much  ? 

22.  A  sold  3432  bushels  of  corn,  which  was  12%  less  than  B 
sold  and  16%  more  than  C  sold.    How  many  bushels  did  B  and 
Csell? 

23.  The  entire  cost  of  goods  was  $207.     The  charges  were 
$17.68  for  freight,  $2.12  for  cartage  and  1%  of  first  cost  for 
insurance.     Find  the  first  cost  of  the  goods  and  what  %  of  the 
first  cost  the  charges  were. 

24..  A  speculator  invested  $4280  in  railroad  stocks.  He  lost 
10%  the  first  year;  gained  15%  the  second  year;  gained  25% 
the  third  year;  lost  5%  the  fourth  year.  Find  the  value  of  the 
investment  at  the  end  of  the  fourth  year. 

25.  A  debtor  paid  me  66f  %  of  his  account.     With  75%  of 
the  money  received  I  bought  a  horse  for  $150.     How  much  was 
the  account? 

26.  A  farmer  sold  20%  of  70%  of  800  bushels  of  wheat  at  $f 
per  bushel.    How  much  money  did  he  receive  ? 

27.  If  $1260  are  gained  by  selling  property  at  a  profit  of 
16f  %,  what  would  be  received  by  selling  it  at  a  loss  of  16f  %  ? 

j    28.  How  much  more  %  is  gained  on  an  article  bought  at  $9 
and  sold  for  $12,  than  on  one  bought  at  $8  and  sold  for  $10? 

29.  35%  of  a  piece  of  land,  40  chains  long  and  35  chains 
wide,  was  sold  at  $22  per  acre;  and  25%  of  the  remainder  was 
sold  at  $19.50  per  acre;  what  now  remained  was  sold  at  $17  per 
acre.  Find  the  total  amount  received. 


PERCENTAGE  181 

SO.  Smith  owned  46%  of  a  farm  worth  $7250.  He  sold  30% 
of  his  share  to  Preston,  and  22%  of  his  share  to  Walker.  Find 
the  value  of  the  land  he  now  owns. 

31.  19%  of  a  merchant's  stock  of  goods  was  destroyed  by 
fire.    He  sold  60%  of  the  remainder  at  25%  profit,  and  sold  what 
now  remained  at  12%  profit.    How  much  did  he  receive,  his  stock 
at  first  being  worth  $4400? 

32.  I  bought  100  yards  of  carpet  at  $.80  per  yard.    I  sold  52 
yards  at  $.92  per  yard,  and  the  remainder  at  15%  profit.     How  * 
many  %  did  I  gain  on  the  whole  lot? 

33.  Davis  raised  1003  bushels  of  potatoes,  which  were  18% 
more  than  80%  of  the  number  of  bushels  King  raised.    Find  the 
number  of  bushels  King  raised. 

34.  Equal  quantities  of  coffee  that  cost  19|  cents,  22 \  cents, 
24J  cents,  and  29£  cents  are  mixed  and  sold  at  30  cents.    What 
is  the  gain  %  ? 

35.  In  a  sum  of  money  containing  $1300,  $585  is  currency, 
$455  is  gold,  and  $260  is  silver.    What  %  of  the  sum  is  in  cur- 
rency; what  %  in  gold;  what  %  in  silver? 

36.  A  merchant  who  began  business  with  $1500,  gained  35% 
the  first  year.     80%  of  the  gain  was  left  in  the  business.     The 
second  year  he  gained  30%  on  what  he  had.    Find  his  capital  at 
the  close  of  the  second  year. 

37.  A  farmer  paid  $720  for  a  horse,  a  wagon  and  a  reaper. 
He  paid  60%  more  for  the  wagon  than  for  the  horse;  and  25% 
more  for  the  reaper  than  for  the  wagon.    How  much  did  he  pay 
for  each  ? 

38.  A  manufacturer  owning  60%  of  a  factory,  sold  12J%  of 
his  share  at  20%  profit  and  received  $1440.     Find  the  value  of 
the  factory. 

39.  Brown  deposited  65%  of  his  money  in  a  bank.    He  paid 
40%  of  the  remainder  to  Myer  on  a  debt,  and  30%  of  what  yet 
remained  for  a  suit  of  clothes;  when  he  found  he  had  but  $14.70 
left    How  much  did  he  have  at  first? 

40.  The  value  of  my  farm  increased  20%,  and  again  25% ; 
then  it  decreased  10%,  and  again  20%.     I  now  sold  for  $2160. 


182  NEW   BUSINESS   ARITHMETIC 

Find  the  original  value  of  the  farm  and  the  amount  I  would  have 
received  if  I  had  sold  after  the  second  increase. 

41.  A  capitalist  has  7-|%   of  his  money  invested  in  U.   S. 
bonds;  12%  in  real  estate;  33J%  in  bank  stock;  15%  in  mort- 
gages; 4%%  in  city  bonds;  $40000  in  telegraph  stock.     He  has 
on  deposit  $3500.    Find  the  value  of  his  property. 

42.  A  paid  $4800  for  two  houses.     20%  of  the  brick  house 
was  equal  to  30%  of  the  frame  house.    Find  the  cost  of  each. 

43.  25%  of  A's  money  is  equal  to  30%  of  B's  money,    and 
40%  of  B's  money  is  equal  to  32%  of  Cs  money.     How  much 
money  has  each,  if  35%  of  Cs  money  is  $252? 

44'  A  dealer  purchased  a  quantity  of  oysters,  fish  and  clams, 
and  paid  for  the  entire  quantity  $166.75.  The  cost  of  the  fish 
was  45%  of  that  of  the  oysters,  and  the  cost  of  the  clams  25% 
of  that  of  the  oysters  and  fish  together.  What  was  the  cost  of 
each? 

45.  The  sales  of  a  firm  were  increased  25%  the  second  year, 
20  %t  the  third  year,  and  16|.%  the  fourth  year.    What  was  the 
amount  of  sales  during  the  first  year,  if  the  fourth  year's  sales 
were  $64442  ? 

46.  The  amount  is  $361.10,  the  percentage  $47.10.    What  is 
the  rate  of  percentage? 


PROFIT  AND  LOSS 

258.  Profit  and  Loss  are  commercial  terms  used  to  express 
the  gain  or  loss  in  business  transactions. 

259.  The  Cost  of  goods  is  the  sum  paid  for  them,  or  the  ex- 
pense of  producing  them. 

The  Prime  Cost  of  an  article  is  its  original  or  first  cost. 

The  Gross  Cost  is  the  original  cost  of  an  article  increased  by 
all  expenses  such  as  freight,  duty,  packing,  commissions,  cartage, 
etc. 

260.  The  Selling  Price  of  goods  is  the  sum  received  for 
them. 

261.  Profit  is  the  sum  above  cost  for  which  goods  are  sold. 

262.  Loss  is  the  sum  below  cost  for  which  goods  are  sold. 
The  gain  or  loss  is  usually  estimated  in  business  transactions 

at  a  certain  %  on  the  gross  cost. 

263.  In  computations  in  profit  and  loss 

1.  Cost  =  Base. 

2.  Gain  or  Loss  =  Percentage. 

3.  Selling  price  at  a  profit  =  Amount. 

4.  Selling  price  at  a  loss  =  Difference. 

The  subjects  of  Profit  and  Loss,  Marking  Goods,  Trade  Discount, 
Commission,  Insurance,  and  Taxes  are  but  applications  of  Percentage. 
Their  problems  may  be  classified  the  same  as  in  Percentage  but  as  these 
classifications  have  been  duly  considered  in  the  study  of  Percentage  they 
will  not  be  repeated  in  these  subjects.  The  pupil  should  endeavor  to 
clearly  understand  the  relations  of  the  parts  of  a  problem  that  are  given 
and  from  these  by  a  process  of  reasoning  determine  the  unknown  or  re- 
quired part.  He  should  learn  as  rapidly  as  possible  to  become  independent 
of  either  formula,  rule  or  classification,  for  in  business  problems  are  not 
presented  tabbed  with  a  rule  nor  classified  by  a  case. 

ORAL  PROBLEMS 

1.  I  paid  $4  for  a  hat  and  sold  it  at  a  gain  of  25%.     How 
much  did  I  gain? 

183 


184  NEW   BUSINESS   ARITHMETIC 

2.  Find  the  gain :    Cost  $84,  sold  at  a  gain  of  10%  ?  20%  ? 

3.  Find  the  loss :    Cost  $60,  sold  at  a  loss  of  20 %  ?  25%  ? 

4.  Find  the  gain  in  the  following :    Cost  $120,  sold  at  a  gain 
of  12%  ?  20%  ?  25%  ?  33J%  ?    Cost  $75,  sold  at  a  gain  of  10%  ? 
30%?  66f%?  25%?     Cost  36  cents,  sold  at  a  gain  of  12|%? 
33J%?     125%? 

5.  Find  the  loss  in  the  following :    Cost  $64,  sold  at  a  loss  of 
12J%  ?  37£%  ?  87|%  ?    Cost  $72,  sold  at  a  loss  of  100%  ?  66f%  ? 
75%  ?    Cost  50  cents,  sold  at  a  loss  of  25%  ?  66f  %  ?  90%  ? 

6.  25  =  iof  what  number?  £?  J?i?i? 

7.  25  =  50%  of  what  number?  33£%  ?  25%  ?  20%  ? 

8.  $40  =  20%  of  what  number?  30%  ?  40%  ?  60%  ? 

9.  In  the  sale  of  a  horse  $25  was  gained.    Find  the  cost  if  the 
sale  was  made  at  a  profit  of  10%?  20%??  25%?  33^%?  50%? 
40%  ?  30%  ? 

10.  A  dealer  gained  $x20  on  a  sale,  which  was  at  a  gain  of 
16|%.    What  was  the  cost? 

11.  24  is  J  more  than  what  number? 

12.  24  is  20%  more  than  what  number? 

13.  $36  is  12  J%  more  than  what  number? 

14.  A  horse  was  sold  for  $150  thereby  gaming  20%.     What 
did  the  horse  cost  ? 

15.  By  selling  berries  at  lOc  per  quart  a  grocer  gains  25%. 
Find  the  cost  of  the  berries. 

16.  A  merchant  sold  potatoes  at  84  cents  per  bushel  thereby 
losing  12J%.    What  did  the  potatoes  cost  per  bushel? 

17.  An  article  cost  $36  and  sells  for  $48.     How  much  was 
gained  ?    What  part  is  the  gain  of  the  cost  price  ?   What  per  cent.  ? 

18.  I  paid  $6  for  each  of  5  chairs  and,  sold  them  for  the  fol- 
lowing sums:    $7,  $8,  $9,  $10  and  $11.    What  was  the  gain  in 
each  case  and  what  was  the  per  cent,  gain? 

19.  A  dealer  paid  $25  for  each  of  4  cows  and  sold  them  for  the 
following  amounts:    $30,  $35,  $40  and  $45.    What  was  his  gain 
per  cent,  in  each  case? 

20.  Find  the  gain  or  loss  per  cent,  in  the  following : 


PROFIT   AND    LOSS 


185 


Cost. 

Selling  price. 

Cost. 

H 

$5. 

$20. 

$6. 

$8. 

$25. 

$7.50 

$10. 

$12.50 

$12. 

$18. 

$50. 

$     .63 

$     .72 

$27.50 

21.  Find 

the  selling  price  in  the  following 

Cost. 

Gain.                               Cost. 

$1000. 

50  % 

$960. 

$50. 

10% 

$40. 

$'2.50 

20% 

$24. 

$30. 

wy*% 

$1600. 

$240. 

6s^% 

$80. 

$10. 

25% 

$62.50 

Selling  price. 

$15. 
$20. 


$24.75 


Loss* 


5% 
1% 


4% 


WRITTEN    PROBLEMS 

264.    1.  A  bill  of  goods  cost  $280  and  was  sold  at  a  profit 
of  25%.    What  was  the  gain? 


SOLUTION 

1.  100%  = 

2.  1%  =  $2.80. 

3.  25%  =  $70. 


Or, 


$280 
.25 

1400 
560 

$70.00 

2.  A  merchant  sold  goods  that  cost  $185  at  a  gain  of  12%. 
Find  his  gain. 

3.  What  is  the  loss  on  goods  that  cost  $140,  and  sold  at  a 
loss  of  18%  ? 

4-  I  bought  170  yards  of  cloth  at  80  cents  per  yard,  and  sold 
it  at  a  gain  of  35%.     Find  my  total  gain. 

5.  A  commission  merchant  bought  210  bbls.  of  apples  at  $2J 
per  bbl.,  and  sold  them  for  9%  less  than  cost.     How  much  did 
he  lose? 

6.  The  loss  on  a  bill  of  goods  was  $21.20,  which  was  4%  of 
the  cost.     Find  the  cost. 


186  NEW   BUSINESS   ARITHMETIC 

7.  Lyman  gained  $58.38  by  selling  at  a  profit  of  14%.    What 
did  the  goods  cost  him? 

8.  A  jeweler  sold  a  ring  for  $2.25  less  than  it  cost,  and  lost 
7|%.    How  much  did  he  pay  for  the  ring? 

9.  A  stock  dealer  bought  26  hogs  that  averaged  285  Ibs.,  at 
7  cents  per  lb.,  and  sold  them  at  1H%  profit.     Find  his  gain. 

10.  Miller  bought  two  horses  for  $80  each,  and  sold  one  at  a 
gain  of  27%,  the  other  at  a  loss  of  19%.    Find  his  net  gain. 

11.  A  quantity  of  tea  was  sold  for  $414,  which  was  10%  below 
cost.     Find  the  cost. 

12.  The  selling  price  is  $360,  the  rate  of  gain  is  20%.     Find 
cost. 

13.  The  selling  price  is  $189,  the  rate  of  gain  is  5%.     Find 
cost. 

14.  The  selling  price  is  $140,  the  rate  of  gain  is  16§%.    Find 
cost. 

15.  A  firm  gained  12%  of  its  capital.     The  amount  of  gain 
was  $1410.     Find  the  firm's  capital. 

16.  A  real  estate  dealer  gained  21^%  by  selling  a  house  for 
•$344  more  than  it  cost  him.    Find  the  cost  of  the  house. 

17.  A  stock  dealer  bought  a  lot  of  cattle  for  $1200,  and  sold 
them  at  a  gain  of  15%.    What  were  they  sold  for? 

18.  A  broker  bought  a  bond  for  $920,  and  sold  it  at  a  gain  of 
17f  %.    Find  his  selling  price. 

19.  The  selling  price  is  $224,  the  rate  of  loss  is  20%.     Find 
•cost. 

20.  The  selling  price  is  $387.20,  the  rate  of  loss  is  12%.    Find 
cost. 

21.  How  much  is  received  for  goods,  bought  for  $355  and  sold 
at  12|%  less  than  cost? 

22.  What  is  gained  by  selling  real  estate  that  cost  $1272,  at 
a  gain  of  8J%  ? 

23.  Hall  sold  a  house  and  lot  to  Miller  for  $650  more  than 
cost,  and  gained  20%.    Miller  sold  it  to  Davis  at  a  gain  of  16%. 
What  did  the  house  cost  each  ? 

#4.  A  grain  dealer  sold  corn  at  33  cents  per  bushel,  thereby 


PROFIT   AND   LOSS  187 

losing  25%.    If  the  entire  loss  was  $825,  how  many  bushels  did  he 
sell? 

25.  The  selling  price  is  $21,  the  rate  of  loss  is  12 \%.     Find, 
cost. 

26.  I  sold  10  acres  of  land  at  27%  gain,  and  received  $825.50 
for  it.    What  was  the  cost  per  acre? 

27.  A  sold  65  yards  of  cloth  for  $89.10,  and  gained  15%. 
Find  the  cost  of  the  cloth  per  yard. 

28.  Ward  sold  his  property  for  $1080,  which  was  33J%  more 
than  it  cost  him.    How  much  did  he  pay  for  the  property? 

29.  I  sold  a  coat  at  a  loss  of  16f  %  and  lost  $4.50.    How  much 
did  I  pay  for  the  coat,  and  what  would  I  have  gained  by  selling 
it  at  a  profit  of  33 J%? 

30.  If  28  yards  of  cloth  are  bought  at  $5.50,  for  how  much 
must  it  be  sold  to  gain  32%? 

31.  A  purchased  a  bill  of  goods  amounting  to  $430.    He  paid 
3%%  for  freight  and  cartage.    For  how  much  must  he  sell  them  to 
gain  13%  on  the  entire  cost? 

32.  Amos  Libby  paid  $30  for  a  cow,  and  sold  it  for  $37.50. 
Find  the  rate  of  gain. 

33.  Hill  lost  $6  on  a  watch  that  cost  him  $75.    What  was  his 
rate  %  of  loss? 

34.  B  bought  a  lot  of  books  for  $60,  and  sold  them  for  $70. 
What  %  did  he  gain? 

35.  I  sold  an  acre  lot  that  cost  $90,  for  $75.60.    Find  my  % 
of  loss. 

36.  C.  W.  Carey  paid  $750  for  a  hall.    He  rented  it  nine  eve- 
nings at  $5  per  evening,  and  then  sold  it  for  $825.     What  was 
his  gain   %? 

37.  A  dealer  sold  125  hogs  at  a  loss  of  8%.     He  received 
$1150    for  them.      How   much   did   he   pay   per   head   for   the 
hogs? 

38.  A   partner's   loss    was   $2250,   which    was   25%    of   his 
investment;  his  investment  was  80%  of  the  firm's  loss.    Find  the 
loss  of  the  firm. 

39.  A  load  of  coal,  costing  $46.50,  was  sold  at  9f%  below 
cost.    Find  the  selling  price. 


188  NEW    BUSINESS    ARITHMETIC 

40.  Snyder  bought  a  house  for  $1370,  and  sold  it  to  Byrne 
at  a  gain  of  19%.    Byrne  sold  it  to  Fuller  at  a  loss  of  8%.    How 
much  did  Fuller  pay  for  the  house  ? 

41.  John  Adams  bought  72  yards  of  cloth  at  $8  per  yard  and 
sold  it  at  a  gain  of  $158.40.    Find  the  rate  %  of  gain. 

42.  A  speculator  sold  a  quantity  of  flour  for  $828.     He  paid 
$920  for  it.    Find  his  rate  %  of  loss. 

43.  B  bought  6  bushels  of  chestnuts  at  $4.50  per  bushel,  and 
sold  4£  bushels  of  same  at  $8.50  per  bushel,  and  the  remainder 
at  $5.25  per  bushel.    What  was  his  rate  of  gain  ? 

44-  How  much  does  a  carriage  dealer  lose  by  selling  a  car- 
riage that  cost  $210  at  a  loss  of  17%  ? 

45.  B  bought  a  bond  for  $1280  and  sold  it  for  42%  more  than 
he  paid.     Find  his  gain. 

46.  Jones  gained  25%  by  selling  a  cow  for  $30  and  lost  18% 
by  selling  another  for  $20.50.    Did  he  gain  or  lose  and  how  much 
on  the  two  cows? 

47.  Johnson  bought  45  sheep  at  $2.50  each.     He  sold  10  at  a 
gain  of  12% ;  12  at  a  gain  of  15%  ;  14  at  a  gain  of  20%  ;  the  re- 
mainder at  a  loss  of  34|%.    How  much  did  he  gain  and  what  % 
did  he  gain? 

48.  A  grocer  bought  eggs  at  27  cents  a  dozen  and  sold  them 
at  the  rate  of  8  for  25  cents.    What  %  profit  did  he  make  ? 

49.  White  sold  a  horse  to  Ellis  at  a  gain  of  25%.     Ellis  sold 
the  horse  for  $75,  which  was  16|%  less  than  the  sum  he  paid. 
How  much  did  the  horse  cost  White  ? 

50.  A  stock  of  goods  were  bought  for  $1840 ;  }  of  the  stock 
was  sold  at  21%  profit;  -J  of  the  remainder  at  24%  profit;  the 
remainder  at  12%  loss.     Find  the  total  amount  received  for  the 
stock. 

51.  25  yards  of  cloth  were  bought  for  $187.50.    At  how  much 
per  yard  must  it  be  sold  to  gain  20%  ;  at  how  much  per  yard  to 
lose  12%  ? 

52.  A  and  B  each  lost  $500  which  was  12%%  of  A's  and  13  J% 
of  B's  money.    Which  had  the  more  money  and  how  much? 

53.  How  much  is  gained  by  purchasing  5  carloads  of  wheat, 


PROFIT   AND   LOSS  189 

of  940  bushels  each,  at  62Jc  per  bushel  and  selling  40%  of  it  at  a 
gain  of  12  J%  and  the  remainder  at  a  gain  of  7-|%  ? 

•    54.  I  sold  a  bill  of  goods  for  $360  and  lost  20%.    Had  I  sold 
60%  at  20%  profit  and  the  remainder  at  12|%  profit,  what  would 

1  have  gained? 

55.  A  merchant  sold  a  bill  of  goods  for  $750  and  lost  6J%. 
What  ought  they  to  have  been  sold  for  to  gain  8%  ? 

56.  A  stationer  bought  3  gross  of  penholders  at  $5  per  gross 
and  retailed  them  at  5  cents  apiece.    What  %  profit  did  he  make  ? 

57.  A  contractor  received  25  cents  a  yard  for  excavating  a 
cellar.    He  paid  his  laborers  21  cents  a  yard.    What  %  profit  did 
he  make? 

58.  Sold  a  horse  at  a  gain  of  33  J%  and  with  the  proceeds 
bought  another  horse,  which  I  sold  for  $120  at  a  loss  of  20%. 
What  did  the  first  horse  cost  me? 

59.  A  merchant's  asking  price  is  25%  above  the  cost.     If  he 
allows  a  customer  a  discount  of  12%  from  the  asking  price,  what 
per  cent,  profit  does  he  make? 

60.  A  merchant  gained  this  year  $1800  which  was   120% 
of  his  gain  last  year  and  that  was  44 -f%  of  his  gain  the  year 
before.    What  were  his  profits  for  the  three  years? 

61.  Sold  pork  at  an  advance  of  1^|% ;  invested  the  proceeds 
in  pork  again,  and  sold  this  lot  at  a  profit  of  16§%,  receiving 
$4627.50.    How  much  did  each  lot  of  pork  cost? 

62.  A  broker  bought  a  quantity  of  wheat  at  $1.12£  per  bushel 
and  sold  the  entire  lot  at  $1.19J  per  bushel.    What  %  profit  did 
he  make? 

63.  A  drover  bought  15  .horses  at  $125  per  head;  and  sold 

2  of  them  at  $127.75  per  head,  8  at  $140  per  head,  and  the  re- 
mainder at  $150  per  head.    If  his  expenses  in  taking  them  to  mar- 
ket were  $5  per  head,  what  was  his  gain  per  cent.  ? 


MASKING  GOODS 

In  Marking  Goods,  merchants  usually  resort  to  some 
device  or  characters  to  conceal  the  cost  and  selling  price  from  the 
customer. 

The  common  method  in  marking  goods  is  to  use  a  word, 
phrase  or  sentence  of  ten  different  letters,  to  represent  the  nine 
digits  and  cipher,  as  a  private  mark.  Characters  other  than  let- 
ters are  also  frequently  used. 

266.  The  Key  is  the  word,  phrase  or  sentence  used  to  rep- 
resent the  nine  figures  and  zero.    An  extra  letter  is  used  to  pre- 
vent the  repetition  of  a  letter,  and  this  is  called  a  repeater. 

The  cost  price  is  usually  written  above  a  horizontal  line  and 
the  selling  price  below.  Fractions  may  be  represented  the  same 
as  whole  numbers. 

267.  Suppose  our  key  is : 

1234567890     repeater, 
chri      stopenx 

cost    $3.18  r.  cp. 

Goods  which  and r-  would  be  marked 

sell  for  $4.46  i.  xt. 

In  the  following  problems  the  quantities  considered  and  meth- 
ods of  solution  are  the  same  as  those  in  Profit  and  Loss. 

1.  My  key  is  "He  saw  it  run."    If  I  pay  $4-.80  per  yard  for 
cloth,  how  must  I  mark  it  to  gain  20%  ? 

2.  Mark  the  cost  and  selling  price  from  the  key  "Now   be 
sharp,"  the  cost  being  $1.40,  and  selling  price  at  a  gain  of  30%. 

Mark  the  cost  and  selling  price  of  the  following  from  the  key 
"You  mark  his." 

3.  Cost  $40,  sold  at  a  gain  of  35%. 

4.  Cost  $1.25,  sold  at  a  loss  of  20%. 

5.  Cost  $2.60,  sold  at  a  gain  of  15%. 

6.  Cost  $90,  sold  at  a  gain  of 

190 


MARKING   GOODS  191 

7.  Cost  $9.50,  sold  at  a  gain  of  60%. 

8.  Cost  $13.50,  sold  at  a  gain  of  52%. 

9.  Knives  bought  at  $4.50  per  dozen,  are  sold  at  35%  profit. 
From  the  key  "Charleston"  mark  the  cost  and  selling  price  of 
each  knife. 

10.  A  merchant  bought  boots  at  $37.50  per  dozen  pairs.    He 
sold  them  at  retail  at  40%  profit.     Mark  the  selling  price  from 
the  key  "Importance." 

11.  Caps  bought  at  $18.75  per  dozen,  are  sold  at  retail  for 
40%  more  than  cost.     Mark  the  cost  and  selling  price  from  the 
key  "Market  sign." 

12.  Mark  the  selling  price  of  collars,  bought  for  $2.70  per 
dozen  and  sold  at  60%  gain,  from  the  key  "The  big  four." 

IS.  Mark  the  selling  price  of  goods  that  cost  $1.46,  and  sold 
at  a  gain  of  45%.    Use  the  key  "He  saw  it  run." 

14.  Goods  marked  from  the  key  "Cash  profit,"  were  sold  at 
a  gain  of  40%.    The  gain  was  a.st.    What  was  the  cost  and  sell- 
ing price? 

15.  I  sold  goods,  marked   from   the  key  "Charleston,"   for 
o.cn,  and  gained  h.en.    What  was  my  rate  of  gain? 

'16.  I  sold  goods  marked  from  the  key  "Hard  moneys"  for 
d.he,  and  gained  10%.    Find  the  cost  and  gain. 

17.  Broadcloth  cost  $2.40  per  yard,  and  is  sold  at  a  gain  of 
25%.     Mark  the  cost  and  selling  price  from    the   key    "Impor- 
tance." 

18.  Goods  marked  from  the  key  "Importance"  were  sold  at 
a  profit  of  25%.     The  gain  was  p.  re.     What  was  the  cost  and 
selling  price  ? 

19.  Mark  the  selling  price  of  shoes,  bought  at  $4.25  and  sold 
at  33J%  profit,  from  the  key  "Gambolines." 

20.  A  merchant  bought  caps  at  auction  at  $10  per  dozen. 
How  will  he  mark  the  selling  price  to  gain  20%,  from  the  key 
"Blackhorse?" 

21.  By  selling  an  article  at  $15  per  dozen  I  gain  20%.    How 
should  I  mark  the  cost  of  each  article    from    the    key    "Cash 
profit?" 


192  NEW   BUSINESS   ARITHMETIC 

22.  A  dealer  bought  12  chairs  for  $12,50  and  sold  them  at 
20%  profit.     How  will  he  mark  the  selling  price,    by    the  key 
"God  help  us?" 

23.  A  merchant  buys  boots  at  auction  at  $37.50  per  dozen 
pairs.     How  shall  he  mark  each  pair  by  the  key  "Market  sign" 
in  order  to  gain  25%  ? 


TKADE  DISCOUNT 

268.  Trade  Discount  is  an  allowance  or  deduction  made  by 
merchants  or  manufacturers  from  their  list  or  marked  price. 

In  issuing  price  lists  and  catalogues  it  is  customary  with  man- 
ufacturers and  large  dealers  to  establish  a  fixed  price,  above  the 
usual  market  price,  and  then  meet  the  fluctuations  in  the  market 
price  by  giving  discounts,  greater  or  less,  from  this  established 
price. 

269.  The  List  Price  or  Invoice  Price  is  the  face  of  the  bill 
before  the  discount  has  been  deducted. 

270.  The  Net  Price  is  the  selling  price  or  the  list  price  less 
the  discount. 

271.  Cash  Discount  is  a  certain  per  cent,  deducted  for  pay- 
ment of  a  bill  immediately,  or  within  a  limited  number  of  days. 

Thus  upon  the  bills  of  a  wholesale  merchant  may  be  seen  the  follow- 
ing :  Terms :  "4  months,  30  days  less  5%"  or  "30  days,  2%  off  10  days," 
which  means  that  purchasers  are  entitled  to  a  credit  of  4  months  but 
will  be  allowed  5%  discount  if  bills  are  paid  within  30  days,  etc. 

272.  The  bill  from  the  jobber  or  manufacturer  frequently 
bears  two  dates ;  a  shipping  date  and  a  date  from  which  sales  com- 
mence.    The  jobbing  and  manufacturing  business  is   from  six 
months  to  a  year  ahead  of  the  wholesale  and  retail  trade.    Goods 
so  sold  and  billed  are  frequently  paid  for  before  the  arrival  of  the 
selling  date  and  if  paid  for  before  that  date  an  additional  discount 
is  deducted.    This  is  called  anticipating  a  bill,  the  rate  is  usually 
the  current  rate  of  interest. 

273.  When  more  than  one  discount  is  given,  the  first  is  reck- 
oned  upon   and   deducted   from   the   list  price,   the   others   are 
deducted  from  the  successive  remainders. 

The  order  in  which  the  discounts  are  deducted  does  not  affect 
the  result.  Thus  a  discount  of  25%,  10%  and  5%  is  the  same  as 
10%,  5%  and  25%. 

274.  It  must  not  be  supposed  that  several  separate  discounts 
are  equal  to  their  sum.    This  is  not  the  case  beca.use  they  are  not 

13  J93 


194  NEW   BUSINESS   ARITHMETIC 

computed  upon  the  same  base.  Thus  25%  and  10%  is  not  the 
same  as  35%. 

In  computations  in  Trade  Discounts  list  price  =  Base. 

275.  To  find  the  net  amount  of  a  bill  when  discounts  are 
allowed. 

ORAL  PROBLEMS 

1.  Find  the  net  in  the  following  single  discounts:    90%,  85%, 
75%,  66f%,  50%,  874%. 

2.  Find  the  net  in  the  following  double  discounts :     10  and 
10%,  25  and  20%,  20  and  20%,  20  and  10%,  33J  and  10%. 

3.  What  is  the  net  price  of  a  piano  listed  at  $300  subject  to  a 
discount  of  10%  ?  25%  ?  30%  ?  12$%  ?  20  and  25%  ?  10  and  10%  ? 
33J  and  10%  ?  50  and  10%  ?  25  and  20  and  10%  ? 

4.  I  bought  a  bill  of  hardware  amounting  to  $120,  subject  to 
a  discount  of  33J%  and  10%.    What  is  the  net? 

5.  A  merchant  paid  $36  for  an  article  which  he  sells  at  an 
advance  of  33^%.     What  must  be  the  asking  price  if  he  allows 
a  discount  of  25%  ? 

WRITTEN    PROBLEMS 

1.  A  bought  a  bill  of  goods  amounting  to  $125.  He  is  al- 
lowed 20%  and  10%  off,  and  5%  off  for  cash.  What  amount  of 
cash  will  pay  the  bill  ? 

SOLUTION  Or, 

1.  100%  -  -  20%  =  80%     $125 

2.  90%  of  80%  =  72%          25        =  20%  discount. 

3.  95%  of  72%  =  68§%   $100"  after  first  discount. 

4.  100%  =  $125.  10        =  10%  discount. 

5.  1%  =  $1.25.  $90  after  second  account. 

6.  68f%  =  $85.50.  4.50  =  5%  discount. 

$85.50         net. 

From  the  foregoing  solution  and  explanation  we  have  the  fol- 
lowing : 


TRADE   DISCOUNT  195 

To  Find  the  Net  Amount  of  a  Bill 

a.  Find  the  net  amount  of  100%. 

b.  Let  100%  equal  the  face  of  the  bill. 

c.  Find  the  ralue  of  1%. 

d.  Find  the  value  of  the  net  amount  of  100%. 

NOTE. — The  net  amount  of  a  bill  may  also  be  found  by  computing  each: 
discount  separately  and  subtracting. 

2.  I  was  allowed  35%  discount  on  a  bill  of  $780.  Find  the 
net  amount  of  the  bill. 

3:  J.  W.  West  sold  a  bill  for  $112.50  on  30  days  time.  He 
accepted  cash  payment  at  a  discount  of  14%.  Find  the  discount 
allowed. 

4.  A.  M.  White  bought  a  reaper  for  $218.40  on  6  months 
time,  or  12J%  off  for  cash.  He  paid  cash.  What  discount  was 
allowed  ? 

•5.  Find  the  net  cost  of  a  bill  of  $187.26  at  a  discount  of 
16§%. 

6.  Smith  bought  an  overcoat,  marked  at  $19.20,  at  a  discount 
of  Yt\%.    What  did  it  cost  him? 

7.  Shoes,  which  were  marked  $6.40,  were  sold  at  12 \%  less 
than  the  marked  price.    How  much  was  received  for  them? 

8.  A  merchant  allowed  me  4J%  discount  on  a  hat,  marked  at 
$2.65.    How  much  did  the  hat  cost  me? 

9.  A  dealer  bought  a  lot  of  coffee  for  $360,  at  a  discount  of 
20  and  10%.    What  was  the  net  cost  of  the  coffee? 

10.  What  single  ctfscount  is  equal  to  a  discount  of  25%,  10% 
and  5%? 

NOTE.— Find  the  net  amount  of  100%  and  subtract  this  from  100%. 

11.  A  discount  of  10  and  5%  is  allowed  on  a  bill  of  $450, 
Find  the  net  cost. 

12.  Owens  sold  Moore  clothing  amounting  to  $234.50,  at  a 
discount  of  20  and  12^%.    What  was  the  net  cost? 

13.  Find  the  net  cost  of  an  invoice  of  $312.90,  at  a  discount 
of  15  and  5%. 

IJt.  B  bought  dry  goods  at  a  discount  of  15,  10  and  6%.  The 
amount  of  the  bill  was  $520.  Find  the  net  cost. 


196  NEW   BUSINESS   ARITHMETIC 

15.  I  was  allowed  a  discount  of  30,  20  and  10%  on  an  invoice 
of  books  amounting  to  $84.    How  much  did  I  pay  for  the  books  ? 

16.  Howard  sold  a  bill  of  notions  for  $760,  with  25,  13  J  and 
8%  off  for  cash.    How  much  cash  did  he  receive? 

17.  How  much  must  I  ask  for  goods  that  cost  $20,  that  I  may 
gain  20%  and  allow  20%  off  from  marked  price? 

Let  100%  =  the  cost  $20,  1%  =  $.20,  120%  =  $24  =  selling  price,  or 
80%  of  marked  price.  If  80%  of  marked  price  =  $24,  1%  of  marked  price 
=  $.30  and  100%  or  marked  price  =  100  X  .30  =  $30. 

18.  Find  the  marking  price  of  goods  that  cost  me  $30,  that  I 
may  gain  20%  and  allow  25%  discount  from  the  marking  price. 

1$.  A  gained  25%  on  goods  that  he  sold  for  40%  discount. 
The  goods  cost  him  $12.  How  much  did  he  ask  for  the  goods? 

20.  B  sold  me  a  bill  of  goods  that  cost  him  $8.40,  at  a  discount 
of  19$%.    He  gained  15%.    How  much  did  he  ask  for  the  goods ? 

21.  What  must  be  the  marked  price  of  goods  that  cost  $5.80, 
that  the  seller  may  allow  5J%  off  and  still  make  a  gain  of  30%? 

22.  The  cost  of  a  pair  of  shoes  was  $1.12.    The  seller  gained 
45%,  and  allowed  a  discount  of  20%.     What    was   his   marked 
price  from  the  key  "Christopen  ?" 


BILLS 

276.  A  Bill  is  a  written  statement  of  merchandise  sold,  or 
services  rendered.     It  should  contain  the  date  and  place  of  pur- 
chase, names  of  the  buyer  and  seller,  and  each  article  with  the 
prices,  terms  and  total  cost. 

277.  An  Item  is  a  single  article  with  price  and  amount,  as 
given  in  a  bill  or  statement. 

278.  An  Invoice  is  a  statement  rendered    by    a    wholesale 
dealer,  or  an  account  of  goods  imported.  The  term  invoice  usu- 
ally refers  to  larger  quantities  of  goods  than  the  term  bill,  but  the 
terms  are  often  used  interchangeably. 

279.  A  Statement  is  a  copy  of  an  account  showing  the  date 
and  amount  of  each  bill  and  also  the  balance  carried  down  from 
the  last  preceding  statement. 

280.  A  Duplicate  Bill  or  Invoice  is  a  copy  of  the  original 
bill.    It  should  always  be  marked  Duplicate  across  its  face. 

To  receipt  a  bill  the  seller  writes  below  the  items  the  words  Re- 
ceived Payment  and  signs  his  name.  If  this  bill  is  receipted  by  a  clerk,, 
who  may  be  authorized  to  perform  such  duties,  he  should  sign  Per  his 
own  name  or  initials  immediately  beneath  that  of  his  principal. 

No.  1 

CHICAGO,  JUNE  18,  1905. 
GEORGE  ADAMS, 

Bought  of  AMOS  BROWN  &  Co. 


3 
5 

25 
10 
2 

bbl.  Minn.  Flour                                    $7.00 
bu.  Potatoes                                               .80 
Ib.  Granulated  Sugar                                  .05 
"   Japan   Tea                                              .65 
box  Florida  Oranges                              4.00 

— 



i 

Received  Payment, 

AMOS  BROWN  &  Co. 
Per  Davis. 

281.    Signs  and  Abbreviations  Used  in  Bills,  Statements,  Etc, 

a\c  or  acct.  account.  C.  O.  D.  collect  on  de-    prox.  next  month. 

@  at  or  to.  livery.  ult.  last  month. 

197 


198 


NEW    BUSINESS    ARITHMETIC 


Ami.    amount. 
bal.  balance. 
Bo't  bought 
B\L  bill  of  lading. 
Co.  Company. 

ctg.   cartage.  int.   interest. 

.contra,  contrary  or  op-    in*t.  present  month. 
posite. 

No.  2 


Cr.  creditor.  Mdse.  merchandise. 

Dr.   debtor.  Pd.  paid. 

E.  and  O.  E.  errors  and    Rec'd  Paym't,  received 
omissions   excepted.  payment. 

F.  O.  B.  free  on  board.    Sunds.  sundries  or  sev- 

eral. 
#number  or  pounds. 


Folio  172.  WORCESTER,  MASS.,  May  1,  1005. 

Sales  Book  345. 

RICHMOND  BROS.  Bought  of  A.  B.  DICKINSON  &  Co. 

Terms  Interest  after  00  days;  2%  discount,  30  days. 


Case 

No.  Yd. 

Price 

Items 

Amount 

#23 

12 

Pieces  Bleached 

Cotton, 

401  432  411  423 

46  471  45s  462 

441  40s  41a  433 

.061 

#5 

15 

Pieces  Muslin, 

331  322  31a  30i 

332  32i  312  34 

- 

333  312  34s  33 

351  323  351 

.07 

#7 

21 

Pieces  Windsor 

Prints, 

233  201  212  22* 

24  232  213  22-' 

242  25  241  231 

202  212  251  243 

203  232  21  253 

26 

.05 

#32 

16 

Pieces  Merrimac 

Prints, 

30  311  322  333 

291  278  282  301 

292  242  272  261 

29s  302  312  33 

.04| 

#11 

6 

Pieces  Delaine, 

391  40  39s  42 

41i  40-". 

.15 



Extend  all  amounts.     What  was  the  cost  if  paid  in  60  days ;  if  paid  in 
30  days;  if  paid  in  cash  with  2  and  2%  off? 

(The  small  figures  at  the  right  represent  fourths — 401  is  40*4  yd.) 


BILLS 

iyy 

No.  3 

Folio  123. 

NEW  YORK,  JAN.  1,  1905. 

Sales  Book  291. 

MR.  M.  I.  PETERSON, 

Bought  of  CLARK  BROS. 

Terms  Cash 

380 

yd. 

Body    Brussels 

@ 

$1.20 

710 

yd. 

Tapestry 

i 

.92 

1% 

yd. 

Moquette  " 

@ 

1.45 

500 

yd. 

3-ply  Ingrain 

@ 

.65 

310 
220 

yd. 
yd. 

2-ply        " 
Matting 

@ 

@ 

.48 
.22 

250 

yd. 

Lining 

@ 

.iii 

Find  what  will  pay  the  bill  with  4  and  4%  off. 

No.  4 

ST.  Louis,  Mo.,  MARCH  11,  1905. 
Folio  367, 
MR.  G.  H.  BROWN, 

Bought  of  JACKSON  BROS. 
Terms  30  days,  10  days  3%  discount,  Cash  3  and  2l/2%  discount. 


2 

Bbl.    25  Prunes  240-20  220 
270-20  250  470     @  .06 

28 

70 

3 

212-19*** 
Bbl.    25  Rice      219-20  ******  @  .08f 
220-20  *  *  * 

4 

Bbl.    20  "A"  Sugar  311  300 
297  288           @  .08* 

5 

Bbl.    20  "G"  Sugar  300  287 
310  303  295    @  .07 

2 

Bbls.    25  Cut  260-18  *** 
Loaf  Sugar                     ***       @  .10 

252-17*** 

3 

Bbl.    25  "C"  310-18*** 
Sugar           320-20******       @  .09 
212-19*** 
Cartage 

2 

What  sum  will  pay  this  bill  at  the  end  of  30  days;  at  the  end  of  10 
days ,  in  cash  when  purchased  ? 

(The  small  figures  at  the  right  of  "Bbl./'  are  the  price  of  the  same.  1st 
item  240-20,  means  that  the  gross  weight  was  240lb.,  allowance  (tare) 
20tb.,  net  Weight  220  tb.  The  2d,  -">th  and  6th  items  are  same  as  1st.) 


200 


NEW   BUSINESS   ARITHMETIC 


No.  5 

Book  4,  Page  411.  SOUTH  OMAHA,  NEB.,  MAY  2,  1905. 

MESSRS.  J.  C.  OLIVER  &  SON, 

Bought  of  L.  B.  SMITH, 
Terms,  60  days,  5%  off  10  days,  4  and  2%  for  cash. 


No.  Lb. 

Price 

Items 

Amount 

6 

Basket    Pork    Loins 

310   313   308  296  301 

299 

.  .07 

4 

Tubs  Lard  68   71   69 

70 

-08| 

3 

Casks  Shoulders  420 

429  427 

•07J 

7 

Bbl.  Mess  Pork 

$17.40 

11 

Casks  Hams  389  3872 

40P    403    392    3973 

4002  398  397  402  400 

.11 

Find  what  sum  will  pay  the  bill  on  July  1 ;  on  May  12 ;  on  date  of  pur- 
chase. 

No.  6 

LYNN,  MASS.,  JUNE  2,  1905. 
MR.  C.  B.  ACKERS, 

Bought  of  P.  T.  BUTLER  &  Co. 
Terms  60  days. 


#  271 

H 

doz.  pr.  Buff  Oxford  Shoes     @  $1.30 

#2710 

6 

doz.  pr.  Ladies'  L.  B.                @    1.40 

#4231 

4 

doz.  pr.  Ladies'  K.  S.  B.           @    2.25 

#1161 
#3210 

5 
3 

doz.  pr.  Farmers'  K.  Boots.     @    3.20 
4%  off 
doz.  pr.  Farmers'  C.  P.  Boots  @    3.00 

#  769 

4 

doz.  pr.  Boys'  Stoga  Boots     @    1.90 

#1279 

2i 

doz.  pr.  Kid  Brogans                @    2.25 

#2128 
#3670 

2 
3 

doz.  pr.  Kip  Plow  Shoes         @    1.85 
5^  off 
doz.  pr.  Custom  Kip  Boots      @    2.10 

#2737 

2 

doz.  pr.  Men's  Thick  Boots     @    3.10 
3^  off 

How  much  cash  will  pay  this  bill  with  3  and  5%  off? 


BILLS  201 

No.  7 

SAGINAW,  MICH.,  JAN.  23,  1905. 
MESSRS.  D.  C.  WILSON  &  Co. 

Bought  of  L.  B.  WRIGHT  &  Co. 

Terms,  Sight  Draft  after  60  days ;  5%  off  if  paid  within  10  days. 


128640  ft. 
33245  ft. 
76898  ft. 
23840 
29300 
33400 
49800  ft. 
96384 
79860  ft. 
29200  ft. 


Pine  Plank 
Clear  Pine 
Clapboards 
Cedar  Posts 
Shingles  "A" 
Shingles  "B" 
Pine  Timber 
Cedar  R.  R.  Ties 
Flooring 
Barn  Boards 


$21.60 

26.80 

24.20 

7.00 

3.80 

3.00 

19.00 

27.00 

24.91 

12.60 


per  M. 
per  M. 
per  M. 
per  C. 
per  M. 
per  M. 
per  M. 
per  C. 
per  M. 
per  M. 


What  is  the  amount  of  the  above  bill,   if  paid  March   10,   1905;   if 
paid  Feb.  1,  1905? 

(M.  means  by  the  1000;  C.  by  the  100.) 

No.  8 

CHICAGO,  ILL.,  SEPT.  26,  1905. 
MESSRS.  BRUNER  &  SON, 

Bought  of  H.  B.  SILVER  &  Co. 
Terms,  90  days,  4%  off,  10  days. 


15 

F.  Base  Burners                         @  $27.50 

12 

K.  Ranges                                  @    30.00 

18 

Cook  Stoves                                @    23.50 

12 

Cook  Stoves                              @    14.00 

8 

Kegs  Nails  "10's"  100#  each    @       .05 

6 

Kegs  Nails  "8's"  100#  each      @        .05* 

2 

doz.  Sets  Knives  &  Forks         @      1.20 

3 

doz.  Sets  Silver  Spoons            @      3.60 

4 

doz.  Tack  Hammers                  @      1.10 





What  is  the  amount  of  the  bill?    What  if  paid  within  10  days?    Wrhat 
if  paid  Oct.  4,  1905,  and  4  and  3#  are  allowed? 


202 


NEW   BUSINESS   ARITHMETIC 

No.  9 


NEW  YORK,  JULY  6,  1905. 
MR.  D.  B.  WARD, 
Bought  of  AMERICAN  BOOK  Co. 
Terms,  30  days. 

18 
24 
30 
12 
36 
18 
12 
12 
12 
12 

24 
18 
6 
12 
12 
12 
24 

New  Practical  Arithmetic          @  $  .68 
"     Primary                               @      .42 
Lessons  in  Grammar  (Welsh)  (g>      .60 
Eclectic  Geography                     @    1.20 
Wright's  Spellers                        @      .26 
Word  Analysis  (Swinton)         @      .35 
Wright's  Alternate  Reader        @      .80 
First                             @      .20 
Second                         @      .28 
Third              "            @      .40 
Less  10# 
Loomis'  E.  Algebra                     @      .55 
C.        "                           @      .85 
Wentworth's  Geometry              @    1.12 
Harkness  Latin  Grammar          @    1.12 
"      Reader              @      .60 
Rice's  Book-keeping                   @    1.60 
Barnes'  Brief  History,  U.  S.      @      .90 
Less  20# 
Cartage 

1 

70 

What  will  the  above  cost  at  4%  discount? 


Folio  828. 
MR.  J.  B.  HINMAN, 

Terms,  30  days. 


No.  10 

GRAND  RAPIDS,  MICH.,  FEB.  14,  1905. 

Bought  of  B.  M.  WESTON  &  Co. 


1 

12 

Bedroom  Sets                              @  $31.50 

6^  off 

20 

Parlor  Sets                                 @    42.00 

H)#  off 

6 

Walnut  Sideboards                    @    16.00 

4£  off 

15 

Walnut  Dining  Tables              @    12.00 

5#  off 

' 

12 

Round  Tables                              @      8.00 

2^  off 

10 

Cherry  Book  Cases                    @     13.50 

3^  off 

18 

Easy  Chairs                                 @      3.20 

12 

Patent  Rockers                           @      5.00 

4%  off 

22 

Baby  Carriages                           («       6.00 

5>  off 

Find  the  cost  of  the  above  at  10  and  2l/>%  off. 


BILLS 


203 


No.  11 

DETROIT,  MICH.,  OCT.  1,  1905. 
MR.  A.  B.  CUM  MINGS, 

Bought  of  R.  K.  MEYERS  &  Co. 
Terms,  April  1,  1906,  60  days,  2%  off  10  days. 


#47 

8     Pieces  Merrimac 
D.  Prints, 
32  312  331  298  301 
31  303  321 

No.  Yd. 

Price 

Items 

Amount 

.05 

#30 

11     Pieces  Gingham, 
341  332  323  31  31  8 
34  331  303  3  I2  32 
33 

.10 

#26 

14     Pieces  Cotton 
Flannel, 
36  352  371  36«  37 
38  373  362  353  361 
372  351  343  35 

.14 

#9 

10     Pieces  Cottonade, 
33  321  312  333  301 
34  293  332  322  323 

.19 

#13 

6     Pieces  Irish  Linen, 
37  371  362  36  372 
353 

.32 

#7 

3     Pieces  Brown 
Duck, 
35  343  351 

.12 

How  much  will  pay  the  bill  April  20,  1906?     How  much  will  pay  the 
bill  on  April  6,  1906? 


MESSRS.  CLARK  &  CHIDESTER, 
Terms,  net  cash  30  days. 


No.  12 

GLOUCESTER,  MASS.,  SEPT.  15,  1905. 

Bought  of  A.  BOOTH  &  Co. 


2 
3 
10 
10 
2 
15 
8 
7 

Qtl.  New  Geo.  Cod                   $  5.75 
bbl.  Ex.  #1  Mackerel                 22.00 
Kits  15  Ibs.  Ex.  #1  "                   1.80 
"    20    "    Bay  #1  "                    1.80 
bbl.  #2  Shore  "         "        lg.       11.75 
Kits  20  Ibs.  #2  shore                     1.55 
Halfs  New  Labrador  Herring   3.67 
"      Round  Shore            "       3.12i 
Box  .25,  Ctg.  .80 

204 


NEW   BUSINESS   ARITHMETIC 

No.  13 


MEYER  VALVE  CO. 
Steam,  Brass  and  Iron  Goods. 

CHICAGO,  July  29,  1905. 
Your  Order  No.  1463. 
Our  Order  No.  9463. 
Terms :  10  da.  2% ;  Net  15  da. 


2 

i  Pt.  SC  Zero  Lub.                     Net  $3.05 

*•** 

2 

1    "     "      "        "                           "      4.25 

*•** 

12 

Filling  Plugs  for  £  Pt.  SC 

Zero  Lub.                                             .35 

*•** 

20* 

•** 

*•** 

12 

i  Coil  Pipe  Syphon                               .50 

#• 

63-10-10* 

*•** 

*•** 

13 

1|  Eng.  Tav  Flue  Cleaners                 2.00 

**• 

80-10-10* 

##•** 

*•** 

1 

2"  Roller  Tube  Expanders                10 

**. 

70-7i-10* 

**•** 

*•** 

2 

2"  Spring  Tube  Expanders                12.00 

**• 

50-5* 

**•** 

**•** 

COMMISSION 

282.  Commission  is  a  compensation  allowed  a  person  who 
buys  or  sells  goods  or  other  property  for  another. 

283.  An  Agent  is  a  person  authorized  to  transact  business 
for,  and  in  the  name  of  another. 

284.  The  Principal  is  the  person  for  whom  an  agent  trans- 
acts business. 

285.  A  Commission  Merchant  is  a  merchant  who  buys  or 
sells  goods,  produce,  live  stock  or  other  property,  as  an  agent  for 
others. 

286.  A  Consignment  is  a  quantity  of  goods  sent  to  a  commis- 
sion merchant  to  be  sold  on  commission. 

287.  The  Consignor  is  the  person  who  sends  the  goods. 

288.  The  Consignee  is  the  commission  merchant  or  person  to 
3vhom  the  goods  are  sent. 

Commission  is  commonly  estimated  at  a  certain  per  cent,  of 
the  amount  of  the  sale  or  purchase.  This  rate  per  cent,  varies 
according  to  the  agreement  of  the  parties  or  the  customs  of  busi- 
ness, and  is  not  fixed  by  law. 

Commission  merchants  are  by  the  customs  of  business  respon- 
sible to  their  principals,  for  the  value  of  goods  sold  by  them  on 
credit.  Xo  separate  rate  per  cent,  is  charged  for  assuming  this 
liability,  but  the  rate  of  commission  is  made  large  enough  to  cover 
it.  In  this  respect  commission  merchants  differ  from  other  agents. 

289.  The  Xct  Proceeds  of  a  sale  or  collection  is  the  amount 
remaining  after  th^  commission  and  other  charges  have  been  de- 
ducted. 

290.  An  Account  Sales  is  a  statement  rendered  by  the  com- 
mission merchant  to  his  principal  after  the  property  has  been  sold, 
showing  the  amount  of  sale,  commission  and  other  charges,  and 
the  net  proceeds. 

291.  A  Remittance  is  a  term  applied  to  the  money  (usually 

205 


206  NEW   BUSINESS   ARITHMETIC 

a  draft) ,  sent  by  the  commission  merchant  to  the  principal  in  pay- 
ment of  the  net  proceeds. 

292.  An  Account  Purchase  is  a  statement  rendered  by  a  com- 
mission merchant  after  goods  have  been  bought,  showing  the  cost, 
charges  and  commission,  and  the  total  or  entire  cost. 

293.  The  Entire  Cost  is  the  sum  of  the  purchase  and  charges. 

The  commission  is  computed  on  the  amount  of  purchase  or  the 
amount  of  sale. 

When  money  is  received,  to  be  invested,  the  amount  received  includes 
the  commission. 

294.  In  computations  in  Commission. 

1.  Amount  of  sale  or  amount  of  purchase  =  Base. 

2.  Commission  =  Percentage. 

3.  Entire  cost  =  Amount. 

4.  Net  Proceeds  =  Difference. 

ORAL  PROBLEMS 

1.  Find  the  commission  at  2%  on  the  following  sales:     $75, 
$64,  $375,  $120,  $320  and  $525. 

2.  Find  the  commission  at  2%%  on  the  following  sales :    $80, 
$240,  $280,  $3.60,  $4.80,  $1200  and  $150. 

3.  After  a  commission  of  3%  is  deducted  from  the  following 
sales,  what  will  be  the  net  receipts:     $75?  $120?  $24?  $60?  and 
$160? 

4.  A  commission  merchant  receives  a  commission  of  $40  for 
selling  some  wheat.    What  did  the  sales  amount  to  if  the  rate  of 
commission  was  2%  ?  2$%  ?  4%  ?  5%  ? 

5.  Find  the  net  proceeds  in  the  following,  sales  $200,  rate  of 
commission  5%  and  various  charges  $15. 

C>.  A  commission  dealer  reports  the  following  sales,  $300. 
Find  net  proceeds,  rate  of  commission  2%  and  $10  charges ; 
24%  and  $12;  3%  and  $18? 

295.  WRITTEN    PROBLEMS 

1.  What  commission  is  received  for  selling  $1250  worth  of 
goods  at  a  commission  of  1%  ? 


COMMISSION  207 

SOLUTION  Or, 

1.  100%  =  $1250.  $1250 

2.  \%  =  $12.50.  .07 

3.  7%  =  $87.50.  $87.50 
From  this  solution  we  deduce  the  following : 

To  Find  the  Commission 

a.  Let  100%  equal  the  amount  of  sale  or  purchase. 

b.  Find  the  value  of  1%. 

c.  Find  the  value  of  the  given  rate. 

Or,  Multiply  the  amount  of  sale  or  purchase  by  the  rate  per 
cent,  expressed  decimally. 

NOTES. — To  find  the  net  proceeds   subtract  the   commission   from  the 
amount  of  sale. 

2.     To  find  the  entire  cost  add  the  commission  to  the  amount  of  sale. 

2.  My  agent  charged  5%  commission  for  buying  merchandise 
worth  $370.     Find  his  commission. 

3.  I  bought  goods  amounting  to  $640  for  A,  and  received 
4f%  commission.  How  much  did  I  receive? 

4.  B  paid  his  agent  6%%  for  buying  goods.     What  was  the 
agent's  commission  on  a  bill  of  $39.50? 

5.  The  amount  of  sale  was  $172.50.     Find  the  agent's  com- 
mission at  3J%. 

6.  White  sold  goods  to  the  amount  of  $28.72  for  me.     I  al- 
lowed a  commission  of  $\%.    Find  the  commission. 

7.  How  much  commission  at  7J%  is  received  on  a  sale  of 
$1282.40? 

8.  A  commission  merchant  sold  185  bbls.  of  apples  at  $5.20 
per  bbl.,  at  a  commission  of  4J%.     Find  the  amount  of  commis- 
sion. 

9.  An  agent  received  ?>\%  commission  for  selling  90  boxes  of 
shoes  at  $12.70  per  box.    What  was  his  commission  ? 

10.  My  agent  bought  170  boxes  of  Jdd  gloves  at  $8.40  per 
box.    How  much  is  due  him  if  he  charges  2f  %  for  buying? 

11.  A's  agent  in  New  York  paid  $1460  for  goods  and  charged 
3%  for  buying  and  2$%  for  insurance.    How  much  did  the  goods 
cost  A  ? 


208  NEW   BUSINESS   ARITHMETIC 

NOTE.  —  Since  he  charged  3%  for  buying  and  2^%  for  insurance,  the 
goods  must  have  cost  105^%  of  the  original  cost.  1%  of  the  original  cost 
is  one  hundredth  of  $1460,  or  $14.60,  and  W52/5%  of  the  original  cost  is 
times  $14.60  or  $1538.84,  the  entire  cost. 


12.  I  sold  $1820  worth  of  goods  for  Brown,  and  charged  him 
3|  %  for  selling.  Find  the  amount  which  was  due  him. 

IS.  The  invoice  price  of  goods  was  $470,  the  agent's  charges 
for  buying  were  §\%.  Find  the  entire  cost. 

14-  A  commission  merchant  bought  eggs  to  the  amount  of 
$128.50  for  Brown  at  a  commission  of  7f  %.  What  did  the  eggs 
cost  Brown? 

15.  An  agent  sold  610  bushels  of  corn  at  30  cents  per  bushel. 
He  charged  a  commission  of  4%.     Find  the  net  proceeds  of  the 
sale. 

16.  A  grain  dealer  sold  through  a  commission  merchant  1000 
bushels  of  wheat  at  84T^  cents    per   bushel.     He    allowed    2f  % 
commission.    Find  the  net  proceeds.  $ 

17.  I  paid  an  agent  $24.60  for  selling  a  quantity  of  flour,  at 
a  commission  of  4.    Find  the  amount  of  the  sale. 


NOTE.  —  Since  4%  of  the  amount  of  the  sale  is  $24.60,  1%  of  the  amount 
of  the  sale  is  one-fourth  of  $24.60  or  $6.15  and  100%  (the  amount  of  the 
sale)  is  100  times  $6.15  or  $615. 

18.  A  received  $36.48  commission  for  buying  goods  for  Gra- 
ham.   How  much  did  the  goods  cost,  if  the  commission  was  3%  ? 

19.  An   agent's  commission  at  2%%   was  $27.50.     Find  the 
amount  of  the  bill  purchased. 

20.  Jones    paid   me   $18.56    for   buying   wheat.     How   many 
bushels  did  I  buy  at  80  cents  per  bushel,  if  my  rate  for  buying 
was  2f%  ? 

,  21.  A  commission  merchant  received  7f%   for  selling.     He 

received  $73.20  commission  on  a  sale.     Find  the  amount  of  the 
sale. 

22.  My  agent  sold  40  cases  of  boots  at  $21.20  per  case,  and 
charged  3§%  for  selling.    Find  the  amount  the  agent  should  re- 
mit to  me. 

23.  What  is  the  selling  price,  if  the  commission  is  $11.48,  the 
rate  being  If  %  ? 


COMMISSION  209 

24.  I  charged  4%  for  selling  some  sheep,  and  received  $37.80. 
How  many  sheep  did  I  sell  at  $3.78  per  head? 

25.  I  shipped  to  a  commission  merchant  140  bbls.  of  potatoes 
and  95  bbls.  of  flour.    He  sold  the  potatoes  at  $2.25  per  bbl.,  and 
the  flour  at  $8.50  per  bbl.     He  charged  4%  for  selling  and  2% 
for  storage.     Find  net  proceeds. 

26.  Find  the  amount  of  purchase,  if  the  entire  cost  including 
3%  commission  is  $309. 

NOTE. — Since  $309  is  3%  more  than  the  amount  of  purchase,  it  is  103% 
of  the  purchase,  1%  of  the  purchase  is  -^s  of  $309  or  $3,  and  100%  (the 
purchase)  is  100  X  $3  or  $300. 

27.  An  agent  remits  $380,  after  deducting  his  commission  of 
5%.    What  was  the  amount  of  sales  ? 

28.  The  entire  cost  was  $676,  the  rate  of  commission  4%. 
Find  the  amount  of  purchase. 

29.  I  sent  my  agent  $341.25  to  invest  in  hogs  at  a  commission 
of  5%.    How  many  hogs  can  he  buy  at  $3.25  per  head? 

30.  B  received  $186.30  to  invest  in  oats  at  30  cents  per  bu. 
He  deducts  his  commission  of  3J%.     How  many  bushels  did  he 
buy? 

31.  A  farmer  received  $164.90  as  the  proceeds  of  the  sale  of 
85  bbls.  of  apples.     For  how  much  per  bbl.  did  the  apples  sell, 
the  commission  being  3%  ? 

32.  A  commission  merchant  sold  115  bu.  of  wheat  at  90  cents 
per  bu.,  240  bu.  of  oats  at  32  cents  per  bu.,  and  665  bu.  of  rye  at 
80  cents  per  bu.    His  charges  were  3%  for  selling,  $24  for  stor- 
age, $9.65  for  drayage,  $15.80  for  demurrage.     What  amount 
should  he  remit  to  the  consignor  ? 

33.  A  commission  merchant  received  $16.74  for  selling  465 
bu.  of  wheat.     For  how  much  per  bu.  did  he   sell   the   wheat   if 
his  rate  for  selling  was  3%  ? 

34.  A  commission  merchant  charged  2f  %  for  selling  and  $6.35 
storage.     He  remitted  $500  to  the  consignor.     Find  the  amount 
of  the  sale. 

35.  What  is  the  selling  price  of  a  house,  if  the  rate  for  sell- 
ing is  8%%  and  the  proceeds  are  $880? 

14 


210  NEW   BUSINESS   ARITHMETIC 

36.  White  remitted  his  agent  $624,  with  instructions  to  buy 
potatoes  at  40  cents  per  bu.,  after  deducting  his  commission  of 
4%.    How  many  bushels  can  he  buy  ? 

37.  An  agent  charged  $14.40  for  buying  an  invoice  of  goods 
amounting  to  $320.    What  was  his  rate  of  commission  ? 

NOTE.— Since  the  cost  $320  is  100%,  $1  is  ^  of  100%  or  i5c%  and  $14.40 
is  14.4  times  &%  or  4l/2%. 

38.  A  commission  merchant  charged  $20.50  including  $7  for 
storage,  for  selling  a  bill  of  $450.    Find  his  rate  of  commission. 

39.  Lyman  purchased  through  an  agent    $218.75    worth    of 
silk.    The  agent  charged  $8.75  for  buying.    What  rate  %  did  he 
charge  for  buying  ? 

40.  The  entire  cost  was  $981.82^,  and  the  commission  was 
$55.57£.    Find  the  rate  of  commission. 

41.  B's  agent  in  Boston  bought  for  him  220  pairs  of  boots  at 
$2.60  per  pair,  and  72  pairs  of  slippers  at  $1.15  per  pair.     His 
commission  was  5J% ;  he  paid  2%   for    insurance,    $33.25    for 
freight,  $7.80  for  drayage.    How  much  did  the  goods  cost  B  ? 

42.  An  agent's  charges  including  $35  for  freight,  were  $78.50, 
and  his  rate  for  buying  was  5%%.     Find  the  amount  of  purchase 
and  the  entire  cost. 

43.  B  collected  60%    of    a    debt.     His    charges    were  $9^30. 
What  was  the  whole  debt,  if  he  charged  1J%  f°r  collecting?  i '  j  0  (/ 

44-  The  entire  cost  of  an  invoice  of  clothing  was  $298.75  in- 
cluding $8.25  for  freight  and  3f%  for  buying.  Find  the  net  cost 
of  the  invoice. 

4-5.  A  commission  merchant  remitted  $358  to  .the  consignor 
after  he  had  deducted  the  following  charges:  5%  for  selling,  2% 
for  insurance,  $4.70  for  cooperage.  What  was  the  selling  price 
of  the  goods  ? 


COMMISSION 

Account  Sales 


211 


CHICAGO,  OCT.  10,  1905. 
Sold  for  account  of  J.  C.  SAMPSON  &  Co. 

By  THOMAS  W.  BANNING. 


190— 

Oct. 

3 

50bbl.  XX  Flour                          6.25 

312 

50 

100     "     Minn.  Flour                       5.75 

575 

M 

10 

100     "    XX  Flour    .                      6.30 

630 

100    "    Minn.  Flour                      5.80 

580 

Charges. 

Oct 

1 

Freight  $67  50  and  Cartage  $15  60 

10 

Storage  350  bbl   @  3c 

a 

10 

Insurance  -fa% 

u 

10 

Commission  5$ 

Net  Proceeds 

Put  the  following  narratives  in  the  form  of  Account  Sales : 
47.  William  C.  Davidson,  Kansas  City,  Mo.,  sold  for  account 
of  Marshall  Field  &  Co.,  Chicago,  the  following  goods:  1905 
Aug.  4,  8  pc.  Summer  Silk,  294  yds.  @  $.72 ;  Aug.  13,  5  pc.  Black 
Silk,  216  yds.,  @  $1.48;  Aug.  17.  16  pc.  Calico,  876  yds.,  @  $.07 ; 
Sept.  3,  19  pc.  Alpaca  548  yds.  @  $.34 ;  Sept.  10,  25  pc.  Diag- 
onals, 587  yds.,  @  $.65.  The  charges  are:  Aug.  1,  Freight  and 
Cartage,  $67.38;  Insurance,  \%  ;  Commission,  5%.  Find  the  net 
proceeds. 

4S.  E.  P.  Ellwood  &  Co.,  Chicago,  sold  for  account  of  Thomas 
Mason  the  following:  1905,  Xov.  1,  300  bu.  Potatoes,  @  48c: 
Nov.  3,  100  bu.,  @  52c ;  Nov.  10,  60  bu.,  @  58c  ;  Nov.  16,  200 
bu.  at  56c;  Dec.  1,  230  bu.  at  57c.  The  charges  are:  Nov.  1, 
Freight,  $86.35 ;  Cartage  at  2c  per  bushel ;  Storage  at  3c  per  bu. ; 
Commission,  5%.  Find  the  net  proceeds. 


212 


NEW   BUSINESS   ARITHMETIC 


49. 


Account  Purchase 


NEW  YORK,  AUG.  16,  1905. 
Bought  for  account  of  DAVID  ANDERSON  &  Co., 

By  HENRY  HAMMOND. 


yd.    Fancy  Prints 
Colored  Silk 
doz.  Ladies'  Felt  Hats 
yd.    Black  Cassimere 
suits  Boys'  Clothes 

Charges. 

Packing  and  Cartage 
Commission  5£ 


.12 

$1.38 

$24.00 

$1.40 

9.00 


Entire  Cost 


Put  the  following  narrative  into  the  proper  form  of  Account 
Purchase : 

50.  A.  B.  Duncan,  St.  Louis,  bought  for  account  of  Davis  & 
Norse  the  following:    1905,  March  18,  150  bbl.  Dakota  Flour  @ 
$5.80;  80  bbl.  Buckwheat  Flour  @  $12.30;  480  bu.  Ground  Feed 
@  30c ;  500  bu.  Bran  @  8c ;  20  bbl.  Superfine  Flour  @  $7.30 : 
Cartage,  $7.80;  Commission,  5%.    What  is  the  entire  cost? 

51.  A  merchant  in  Peoria  shipped  to  his  broker  in  Chicago 
a  car  lot  of  potatoes,  967  bu.,  which  were  sold  at  64c  per  bushel. 
What  was  realized  on  the  sale  if  the  broker  charged  5%    for 
selling  and  freight  cost  4c  per  100  Ibs.  ?    How  many  pounds  of 
Golden  Rio  coffee  could  be  purchased  with  the  proceeds  of  the 
sale  of  potatoes  if  coffee  is  worth  12c  per  pound  and  the  broker 
charges  a  commission  of  3%  for  buying? 


INSURANCE 

296.  Insurance  is  a  security  guaranteed  by  one  person  or 
company  to  another,  against  loss  or  damage. 

The  several  kinds  of  insurance  derive  their  names  from  the 
kinds  of  risks  assumed ;  thus  we  have  Fire  Insurance,  Marine  In- 
surance, Life  Insurance,  Health  Insurance,  etc. 

There  are  several  other  minor  forms  of  property  insurance,  such  as 
Live  Stock  Insurance,  Tornado  Insurance,  Steam  Boiler  Insurance,  Plate 
Glass  Insurance,  etc.,  the  nature  of  which  is  indicated  by  their  names. 

297.  Accident  Insurance  is  security  against  loss  or  damage 
by  accident  in  traveling. 

298.  Life  Insurance  secures    a    certain    sum    to    a    person's 
heirs  in  case  of  death. 

299.  Health  Insurance  secures  an  allowance  during  sickness. 

300.  The  Insurer  or  Underwriter  is  the  party  who  agrees  to 
make  good  the  loss  or  damage. 

301.  The  Insured    is    the    person    secured    against    loss    or 
damage. 

Insurance  is  usually  conducted  by  companies  organized  for  the 
purpose  and  these  may  be  classified  as  Stock  Companies  and 
Mutual  Companies. 

302.  A  Stock  Company  is  one,  the  capital  of  which  is  owned 
by  individuals  called  stockholders,  who  alone  share  the  profits  and 
losses. 

303.  A  Mutual  Company  is  one  in  which  the  insured  becomes 
a  sharer  in  the  losses  and  gains  of  the  company. 

Some  companies  combine  the  principles  of  Stock  and  Mutual  Com- 
panies and  are  termed  Mixed  Companies. 

304..  The  Policy  is  the  written  contract  between  the  insurer 
and  the  insured.  It  describes  the  property  insured,  the  conditions, 
time,  rate,  etc. 

305.  A  Valued  Policy  is  one  in  which  the  value  of  the  prop- 
erty insured  is  specified. 

213 


214  NEW   BUSINESS   ARITHMETIC 

306.  An  Open  Policy  is  one  in  which  the  value  of  the  prop- 
erty insured  is  to  be  determined  after  loss.     This  arises  usually 
in  cases  of  merchandise  in  transit,  and  enables  merchants  to  in- 
sure property  shipped  at  different  times  and  places. 

307.  The   Premium   is  the   sum   paid   for   insurance   and   is 
usually  a  certain  rate  per  cent,  on  the  amount  insured. 

The  rates  of  premium  depend  upon  the  character  of  the  risk, 
and  the  length  of  time  it  has  to  run.  The  rate  for  three  years  in 
fire  companies  is  usually  twice  the  rate  for  one  year. 

FIRE  INSURANCE 

308.  Fire  Insurance  is  a  security  against  loss  or  damage  by 
fire. 

Fire  insurance  covers  not  only  loss  by  fire,  but  also  from  smoke,  water 
used  in  putting  out  a  fire  in  an  adjoining  building  and  breakage  or  dam- 
age done  by  firemen  while  arresting  the  progress  of  a  fire,  such  as  blow- 
ing up  a  building. 

Whoever  owns  or  has  an  interest  in  property,  may  insure  it  to  the  full 
amount  of  his  interest  or  ownership. 

No  more  than  the  actual  loss  can  be  recovered  by  the  insured,  whether 
there  be  one  or  several  insurers. 

Usually  property  is  insured  for  about  thr.ee-fourths  of  its  actual  value. 

309.  Adjustment  of  Losses.     Fire  insurance  companies,  as 
a  rule,  pay  the  full  amount  of  the  loss,  provided  this  does  not 
exceed  the  valuation  named  in  the  policy.     Some  policies  contain 
the  ''average  clause"  which  requires  the  payment  of  only  such 
a  portion  of  the  loss  as  the  amount  insured  bears  to  the  whole 
value  of  the  property. 

Thus,  under  the  "average  clause/'  if  property  worth  $10000  is  insured 
for  Y-2.  its  value  or  $5000,  the  company  will  in  case  of  loss,  pay  but  y*  of 
the  loss  whereas  without  the  "average  clause"  the  company  would  pay 
the  entire  loss  up  to  the  limit  of  $5000,  or  the  face  of  the  policy. 

In  Chicago  the  board  of  underwriters  have  inserted  an  "80%  clause" 
in  policies,  which  exempts  the  policy  from  the  "average  clause"  in  case 
the  insured  shall  carry  insurance  equal  to  80%  of  the  value  of  the  property. 

31 0..  In  computations  in  Fire  Insurance, 
J.  Valuation  =  Base.    2.  Premium  =  Percentage. 
311.  To  find  the  premium  when  the  valuation  and  rate  of  in- 
surance arc  giren. 


INSURANCE  215 

ORAL  PROBLEMS 

1.  What  is  the  premium  at  2%   on  the   following:     $1200, 
$350,  $750,  $3000? 

2.  What  is  the  premium  at  2±%  on  the  following :    $400,  $T50, 
$600,  $1500,  $900? 

3.  A's  house  cost  $6000.     What  is  the  premium  at  \\%  on  a 
three-fourths  valuation  ? 

4-  I  paid  $4  premium  for  insuring  household  goods  at  1%. 
What  was  the  face  of  the  policy  ? 

5.  What  is  the  insurance  on  a  building  if  the  premium  at  2±% 
is  $75? 

6.  A  house  valued  at  $3200  was  insured  at  a  three-fourths 
valuation  for  a  term  of  3  years.     What  was  the  premium,  the 
rate  being  1J%  per  year? 

7.  If  $72  is  paid  for  insurance  for  4  years,  what  is  the  policy 
if  the  rate  is  2%  ? 

WRITTEN    PROBLEMS 

1.  A  insured  a  house  for  $8400  at  \%  premium.     What  was 
the  premium? 

SOLUTION  Or, 

1.  100%  =  $8400.  $8400 

2.  1%  =  $84.  .OOf 

3.  \%  =  $63,  the  premium.  $63.00 

We  therefore  have  the  following  rule : 

To  Find  the  Premium 

a.  Let  100%  equal  the  valuation. 

b.  Find  the  value  of  1%. 

c.  Find  the  value  of  the  given  rate. 

Or,  Multiply  the  valnation  by  the  rate  per  cent,  expressed  deci- 
mally. 

2.  A  house  is  insured  for  $6400  at  2$%.     What  is  the  pre- 
mium ? 

3.  A  insured  a  house  for  $2400  and  its  contents  for  $800  at 
35&.     What  was  the  premium? 


216  NEW   BUSINESS   ARITHMETIC 

4-  A  merchant  insured  a  stock  of  good,s  worth  $4500  for  § 
of  their  value  at  2%%.    What  was  the  premium? 

5.  A  building  worth  $28400  is  insured  for  f  of  its  value  at 
'3%.    What  is  the  premium  ? 

6.  What  will  it  cost  to  insure  a  barn  worth  $4200  for  f  its 
value  at  \%1 

7.  A  has  $1240  worth  of  live  stock  insurance  at  §%  ;  store 
worth  $5200  insured  at  \\%  ;  stock  of  merchandise  worth  $2700 
insured  at|%.    How  much  premium  does  he  pay? 

8.  A  house  valued  at  $2640  was  insured  for  f  its  value  at 
&%,  and  furniture  valued  at  $1650  for  f  its  value  at  \\%.     If 
the  property  is  burned  and  the  company  pays  the  loss,  what  will 
be  the  net  loss  to  the  company  ? 

9.  I  paid  a  premium  of  $72  for  insuring  merchandise  at 
What  was  the  amount  insured  ? 


NOTE.  —  Since  the  premium  is  1^4%  and  amounts  to  $72,  1J4%  ~  $72,  and 
1%  equals  as  many  dollars  as  ll/4  is  contained  times  in  $72  or  $57.60  and 
100%,  the  amount  insured,  equals  100  times  $57.60  or  $5760. 

10.  Smith  paid  $51.75  premium  for  insurance  on  his  property 
for  f  its  value  at  -f^%.    What  was  the  value  of  the  property? 

11.  If  a  company  charges  $60  for  insuring  a  building  for  f 
its  value  at  If  %,  what  is  the  amount  of  the  policy  and  the  value 
of  the  property? 

12.  A  barn  insured  for  $2850  for  5  years  at  75c  per  annum 
was  destroyed  by  fire.    What  was  the  actual  loss  of  the  company  ? 

IS.  A  stock  of  goods  worth  $9500  is  insured  for  $6500,  and 
is  damaged  by  water  while  extinguishing  a  fire  in  an  adjoining 
building  to  the  amount  of  $1.320.  The  policy  contains  an  "average 
clause."  What  amount  will  the  company  pay? 

14.  A  insured  his  stock  of  goods  as  follows:  $2000  in  the 
y£tna  Insurance  Company,  $2800  in  the  Home  Insurance  Com- 
pany, $3500  in  the  Essex  Company,  $4200  in  the  Phcenix  Com- 
pany. His  loss  by  fire  was  $4375.  How  much  will  each  company 
pay? 

NOTE.  —  Find  the  total  insurance.  Find  what  per  cent,  the  loss  is  of  the 
total  insurance.  Multiply  each  risk  by  the  per  cent,  of  loss. 


INSURANCE  217 

15.  A  building  was  insured  in  the  Mutual  Company  for  $2700, 
in  the  Springfield  Company  for  $3600,  in  the  Local  Company  for 
$4000,  in  the  Commercial  Company  for  $5400.     A  loss  of  $3611 
was  caused  by  fire  and  water.    What  loss  was  paid  by  each  com- 
pany? 

16.  The  loss  by  fire  and  water  on  the  Union  National  Bank 
building  was  $68340.     It  was  insured  as  follows:     Metropolitan 
Company  $18000;  Great  Western  Company  $22000;  American 
Company  $13000;  United    States    Company    $15000;    Lancaster 
Company  $25000;  Orleans  Company  $9000.     How  much  of  the 
loss  is  paid  by  each  company  ? 

17.  I  paid  a  premium  of  $102  for  insurance  on  my  house  for 
f  its  worth  at  2J%.    What  was  the  house  worth  and  what  would 
be  the  company's  net  loss,  if  the  property  was  destroyed  ? 

18.  I  paid  $124.80  for  having  a  building  worth  $6800  insured 
at  f  its  value  and  its  contents  valued  at  $8200  insured  at  f  their 
value.    What  rate  did  the  company  charge  for  insuring  ? 

19.  A's  house  worth  $2500  was  insured  for  f  its  worth,  and 
furniture  worth  $3690  for  f  its  worth.    The  premium  was  $70.40. 
What  was  the  rate  of  insurance? 

20.  A  farmer  had  his  horses  worth  $960  insured  for  their 
full  value ;  his  cows  worth  $1260  insured  for  f  their  value ;  his 
hogs  worth  $822  insured  for  %  their  value.     What  was  the  rate 
of  insurance  if  he  paid  a  premium  of  $89.46? 

MARINE   INSURANCE 

312.  Marine  Insurance  is  a  security  against  loss  or  damage 
to  vessels  and  their  cargoes  by  the  perils  of  navigation. 

Transit  Insurance  is  security  against  loss  or  damage  to  prop- 
erty while  in  transit  by  railroad  or  water  route  and  is  a  kind  of 
marine  insurance. 

313.  An  Insurance  Certificate  is  a  document  issued  by  marine 
insurance  companies  similar  in  nature  to  a  policy. 

Insurance  certificates  are  negotiable  and  are,  together  with 
bills  of  lading,  used  by  shippers  as  security  for  money  advanced 
by  banks. 


218  NEW    BUSINESS    ARITHMETIC 

314.  Policies  on   cargoes   are   issued   for  a   certain   voyage 
and  on  vessels  for  a  specified  time. 

315.  Adjustment  of  Losses.     In  Marine  Insurance  the  com- 
pany pays  in  case  of  loss,  such  proportion  of  the  loss  as  the 
amount  of  the  policy  bears  to  the  value  of  the  property.    Thus  if 
the  property  is  insured  at  ^  its  value,  the  company  pays  \  of  the 
loss.     This  is  upon  the  principle  of  the  "average  clause." 

Merchants  are  usually  provided  with  open  policy  books,  which  are 
used  under  the  terms  of  an  open  policy  and  in  which  they  enter  each  ship- 
ment as  soon  as  the  invoice  is  received.  At  the  end  of  the  month  these 
books  are  collected  by  the  company  or  its  agent,  the  entries  transferred 
to  their  books  and  a  bill  rendered  the  merchant  for  the  premium. 

Computations  in  Marine  Insurance  are  based  upon  the  princi- 
ples of  Percentage  the  same  as  in  Fire  Insurance. 

1.  A    ship    is    insured    for    $85000    at    2J%.      What    is    the 
premium  ? 

2.  A  ship  is  insured  for  $35000  at  \\%  and  her  cargo  is  in- 
sured at  $55000  at  Z\%.    What  is  the  total  premium? 

3.  A  cargo  of  good,s  was  insured  for  $10200,  at  1%.     What 
was  the   premium? 

4.  A  shipment  of  merchandise  from  New  York  to  Chicago 
worth  $20000  is  insured  for  $15000  at  \%.    It  is  damaged  to  the 
amount  of  $4200.    What  is  the  company's  net  loss  ? 

5.  What  amount  must  be  paid  for  insuring  a  cargo  of  mer- 
chandise for  $2500  at  $1.15  and  another  cargo  of  $3700  at  $1.20, 
less  15%  discount  on  both  premiums? 

6.  A  vessel  worth  $37500  was  insured  for  $10000  in  one  com- 
pany at  3%  premium,  and  for  $17500  in  another  at  \%  premium. 
She  was  afterwards  damaged  by  a  storm  to  the  extent  of  $3000. 
Find  the  owner's  loss  including  premium  paid. 

7.  A  New  York  merchant  sent  goods  worth  $1186  by  water  to 
Chicago.     He  insured  them  for  $800  at  1J%>.     They  are  dam- 
aged to  the  extent  of  $235.     What  amount  does  the   owner    lose 
including  premium  paid? 

8.  A  vessel  and  cargo  worth  $48640  were  insured  in  the  fol- 
lowing companies,  as  follows :    $4500  in  the  Paoli ;  $7200  in  the 


INSURANCE  219 

Leipsic;  $8600  in  the  West  Baden;  $3350  in  the  Custer ;  $6750  in 
the  Litchfield.  The  vessel  and  cargo  sustained  a  loss  of  $17936. 
What  amount  was  paid  by  each  company  ? 

LIFE  INSURANCE 

31G.  Life  Insurance  secures  a  certain  sum  of  money  to  be 
paid  to  a  person's  heirs  in  case  of  his  death,  or  to  himself,  should 
he  survive  a  certain  number  of  years. 

317.  The  Policy  is  the  written  contract  between  the  parties, 
and  sets  forth  the  conditions  of  the  agreement. 

318.  The   Ordinary  Life  Policy   requires  payments  of  pre- 
mium during  life,  and  the  policy  is  payable  only  upon  the  death 
of  the  insured. 

319.  The   Limited  Payment  Life  Policy   requires   premium 
to  be  paid  for  only  a  specified  number  of  years,  as  five  years  or 
ten  years,  policy  payable  at  death. 

320.  The  Endowment  Policy  is    payable    at    the    end    of   a 
specified  number  of  years  or  before  if  insured  should  die. 

321.  The  Annuity  Policy  secures  by  a  single  payment  of 
premium,  the  payment  to  the  insured  of  a  certain  sum  annually 
during  his  lifetime. 

322.  The  Beneficiary  is  the  person  to  whom  the  policy  is 
made  payable. 

323.  The  Insured  is  the  person  whose  life  forms  the  subject 
matter  of  the  policy. 

A  person  may  insure  his  own  life  or  that  of  any  person  in  whom  he 
has  a  pecuniary  interest,  or  upon  whom  he  depends  for  support,  as  that 
of  a  near  relative,  or  debtor  to  the  amount  of  the  debt  existing.  But  a 
person  cannot  insure  the  life  of  a  stranger  or  one  in  whom  no  pecuniary 
interest  exists. 

324.  The  Surrender  Value  of  a  policy  is  the  amount  of  cash 
which  the  company  will  pay  the  holder  at  any  time  upon  the  sur- 
render of  the  policy. 

325.  The  Expectation  of  Life  is  the  number  of  years  that 
a  person  of  a  given  age  will  probably  live,  based  upon  the  records 
of.  mortality. 


220 


NEW   BUSINESS   ARITHMETIC 


TABLE  OF  RATES. 


Annual  Premium  for  an  Insurance  of  $1,000. 


LIFE  POLICIES 

ENDOWMENT  POLICIES 

u 
< 

Annual 
Premium 

10  Annual 
Payments 

15  Annual 
Payments 

20  Annual 
Payments 

10-Year 
Endowment 

15-Year 
Endowment 

'  20-  Year 
Endowment 

25-Year 
Endowment 

30-Year 
Endowment 

~25~ 

$20  50 

$43  50 

$33  10 

$28  10 

$105  90 

$67  40 

$48  70 

$38  00 

$31  40 

26 

21  00 

44  30 

33  80 

28  60 

106  00 

67  50 

48  90 

38  20 

3?  60 

27 

21  50 

45  20 

34  40 

29  20 

106  10 

67  60 

49  00 

38  40 

31  80 

28 

22  10 

46  10 

35  10 

29  80 

106  30 

67  80 

49  20 

38  60 

3?  00 

29 

22  70 

47  00 

35  90 

30  50 

106  40 

68  00 

49  40 

38  80 

32  30 

30 

23  30 

48  00 

36  60 

31  10 

106  60 

68  20 

49  60 

39  10 

32  60 

31 

24  00 

49  10 

37  40 

31  80 

106  80 

68  30 

49  80 

39  30 

32  90 

32 

24  70 

50  10 

38  30 

32  60 

107  00 

68  60 

50  10 

39  60 

33  20 

33 

25  50 

51  20 

39  10 

33  30 

107  20 

68  80 

50  30 

39  90 

33  60 

34 

26  30 

52  40 

40  00 

34  10 

107  40 

69  00 

50  60 

40  30 

34  00 

35 

27  10 

53  60 

41  00 

35  00 

107  60 

69  30 

50  90 

40  60 

34  50 

36 

28  00 

54  80 

42  00 

35  80 

107  80 

69  60 

51  30 

41  10 

35  00 

37 

29  00 

56  20 

43  00 

36  80 

108  10 

69  90 

51  70 

41  50 

35  60 

38 

30  00 

57  50 

44  10 

37  70 

108  40 

70  20 

52  10 

42  00 

36  20 

39 

31  10 

59  00 

45  30 

38  80 

108  70 

70  60 

52  50 

42  60 

36  80 

40 

32  20 

60  40 

46  50 

39  80 

109  10 

71  00 

53  00 

43  20 

37  60 

41 

33  40 

62  00 

47  70 

41  00 

109  40 

71  50 

53  60 

43  90 

38  40 

42 

34  70 

63  60 

49  00 

42  20 

109  80 

72  00 

54  20 

44  60 

39  30 

43 

36  10 

65  30 

50  40 

43  50 

110  30 

72  50 

54  80 

45  40 

40  30 

44 

37  50 

67  10 

51  90 

44  80 

110  80 

73  10 

55  60 

46  30 

41  30 

45 

39  10 

69  00 

53  40 

46  20 

111  30 

73  80 

56  40 

47  30 

42  50 

46 

40  70 

70  90 

55  10 

47  80 

112  00 

74  60 

57  30 

48  40 

43  80 

47 

42  50 

72  90 

56  80 

49  40 

112  60 

75  40 

58  30 

49  60 

45  20 

48 

44  40 

75  10 

58  60 

51  10 

113  40 

76  30 

59  40 

51  00 

46  80 

49 

46  40 

77  30 

60  50 

52  90 

114  20 

77  30 

60  70 

52  40 

48  50 

50 

48  50 

79  60 

62  50 

54  80 

115  10 

78  40 

62  00 

54  00 

50  30 

To  find  the  annual  premium  which  must  be  paid  on  a  policy 
of  $1000,  look  in  the  left  hand  column  under  Age  and  find  the  age 
of  the  insured,  then  opposite  this  look  in  the  column  descriptive 
of  the  policy  and  the  amount  will  be  the  premium  on  $1,000, 
which  multiplied  by  the  thousands  and  decimals  of  thousands  of 
dollars  in  the  policy  will  give  the  premium  required. 

1.  A  man  at  the  age  of  40  desires  to  take  out  an  ordinary  life 
policy  for  $5000.    What  is  the  premium  ? 


INSURANCE  221 

2.  What  is  the  premium  on  a  policy  for  $4250,  the  insured 
being  33  years  of  age,  by  the  15  payment  life  plan? 

3.  What  will  be  the  annual  premium  for  $2500  on  a  person's 
life  at  the  age  of  26,  for  15  years,  under  the  endowment  plan? 

4.  A.  B.  Smith,  35  years  of  age,  desires  to  take  out  an  en- 
dowment policy  payable  in  25  years  for  $1500.    What  will  it  cost 
him  annually? 

5.  A  teacher  at  the  age  of  32  years  had  his  life  insured  for 
$3000  by  the  ordinary  life  plan  and  died  after  making  13  pay- 
ments.   How  much  did  his  family  receive  more  than  he  had  paid 
the  company? 

6.  A  person  aged  29  years  takes  out  an  endowment  policy  for 
$8000  payable  in  20  years.    He  lived  past  the  endowment  period. 
What  did  he  gain,  having  paid  his  premium  regularly,  making 
no  allowance  for  risk  or  interest  on  payments  ? 

7.  A  gentleman  in  Chicago,  32  years  of  age,  wishing  to  pro- 
vide for  his  family  in  case  of  his  death,  obtains  a  life  policy  for 
ten  years  for  $3090.     What  amount  of  annual  premium  must  he 
pay? 

S.  If  I  take  an  endowment  policy  of  $3000  at  the.  age  of  28, 
payable  to  myself  in  20  years,  and  the  dividends  increase  the 
policy  $912.25,  how  much  more  will  I  receive  from  the  company 
than  I  have  paid? 

9.  A  gentleman,  45  years  of  age,  gets  his  life  insured  for 
$5000,  by  the  20  year  endowment  plan,  and  dies  at  the  age  of  50 
years.  How  much  more  has  his  insurance  cost  him  than  it  would 
have  cost  by  the  ordinary  life  plan? 

10.  John  Davidson,  age  32,  takes  out  a  25  year  endowment 
policy  for  $5000.     At  37  years  of  age  he  takes  out  a  10  year 
endowment  for  $5000.     At  42  years  he  takes  out  a  15  year  life 
policy  for  $5000.    What  are  his  total  annual  premiums  after  taking 
out  his  last  policy? 

11.  A  man  aged  38  years  secured  a  life  policy  for  $8000. 
After  making  7  annual  payments  he  died.    How  much  more  than 
the  amount  of  premium  paid  was  received  by  the  heirs  of  the  per- 
son insured? 


222  NEW   BUSINESS    ARITHMETIC 

12.  Amos  Duncan,  aged  25  years,  takes  out  a  20  year  endow- 
ment for  $2500.  Assuming  that  he  will  live  to  receive  the  policy 
how  much  more  will  he  receive  than  he  pays  the  company? 

REVIEW  PROBLEMS  IN  PERCENTAGE 

326.  1.  What  %  is  gained  by  selling  f  of  a  barrel  of  flour 
for  g-  of  what  the  barrel  cost  ? 

2.  If  B  loses  25%  by  selling  his  horse  for  $80,  for  how  much 
must  he  sell  it  to  gain  40%  ? 

3.  I  lost  $62.40  by  selling  60  bbls.  of  flour  at  24%  less  than 
cost.    What  was  the  cost  per  bbl.? 

4.  A  has  $1600.    75%  of  his  money  is  equal  to  62£%  of  B's 
money.    How  much  have  both  together? 

5.  What  is  the  cost  of  an  article  on  which  25%  is  gained, 
after  deducting  40%  from  the  marked  price,  which  is  $10? 

6.  B  sold  his  horse  for  $105,  which  was  £  of  its  cost.    What 
'%  would  he  have  gained  by  selling  it  at  $109.80? 

7.  By  selling  shoes  at  $2.30  per  pair,  8%,  is  lost.     At  what 
price  per  pair  must  they  be  sold  to  gain  12%  ? 

S.  What  %  does  a  merchant  gain  by  selling  hats  at  $1.40, 
that  were  bought  at  $18  per  dozen  less  20  and  12J%  ? 

9.  A  clothier  reduced  the  price  of  an  overcoat  90  cents,  and 
thereby  reduced  his  profit  from  15%  to  10-|%.  How  much  did  it 
cost  him? 

10.  Lyman  paid  30%  of  his  debt,  and  then  found  that  $?OS 
would  pay  65%  of  the  remainder.     What  was  the  amount  of  the 
debt? 

11.  I  bought  goods  at  J  of  their  value  and  sold  same  at  18% 
more  than  their  value,  and  received  $3776.    What  did  I  pay? 

12.  From  the  key   "Have   it   snow,"  mark  goods  that  cost 
$1.52,  that  I  may  gain  25%  and  allow  5%  from  the  marked  price. 

IS.  What  is  my  rate  of  annual  income  on  $1905  invested  in 
real  estate  which. rents  for  $15  per  month,  allowing  $27.60  taxes 
and  repairs? 

14.  What  must  be  the  marked  price  of  hats  that  cost  $2.10, 
that  10%  may  be  deducted  from  the  price,  and  yet  a  profit  of  20% 
be  made  ? 


REVIEW    PROBLEMS  228 

15.  What  %  is  gained  by  buying  goods  at  a  discount  of  20 
and  25%,  and  selling  same  at  a  discount  of  10  and  5%  ? 

16.  A  merchant  sold  goods  at  5%  less  than  marked  price  and 
yet  made  a  profit  of  25%.     The  marked  price  was  what  %  ad- 
vance on  cost  ? 

17.  I  sold  wheat  at  a  profit  of  15% ;  invested  the  amount  re- 
ceived in  wheat  again,  and  sold  it  at  a  profit  of  18%,  receiving 
$1709.82.    How  much  did  each  lot  cost  me? 

IS.  An  agent  sold  real  estate  on  his  own  account  for  $2780, 
and  gained  15%.  For  how  much  should  he  have  sold  it  to  gain 
25%? 

19.  A  merchant  whose  average  profits  were   12%,  sold  his 
business  and  loaned  his  money  at  7-|%.    His  annual  income  is  re- 
duced $427.50.    Find  his  investment. 

20.  A  clothing  merchant  paid  $4.80  for  a  coat  and  marked  it 
so  that  he  could  allow  25  and  20%  discount  and  yet  gain  30%. 
What  was  the  marked  price  ? 

21.  A  wholesale  merchant  sells  goods  at  retail  at  40%  above 
cost  and  at  wholesale  at  15%  less  than  retail  price.     What  is  his 
gain  %  on  goods  sold  at  wholesale  ? 

22.  I  received  $5.80  less  for  goods  sold  at  12%  loss,  than  I 
would  have  received  had  I  sold  at  17%  profit.    How  much  would 
be  received  for  the  goods  at  30%  profit? 

23.  An  agent  sold  corn  at  4%  commission  and  invested  the 
proceeds  in  coffee  at  5%  commission;  his  total  commission  was 
$312.    Find  the  selling  price  of  the  corn  and  the  cost  of  the  coffee. 

24.  My  room  is  30  feet  wide,  and  its  length  is  40%  longer 
than  the  width.    I  carpet  it  with  carpet  £  of  a  yard  wide.   What 
is  the  cost  at  60c  a  yd.,  laid  lengthwise?     Laid  crosswise? 

25.  Wilson  sold  a  piano  to  Davis  at  a  gain  of  25%.     Davis 
sold  the  piano  for  $350,  which  was  12|%  less  than  the  sum  he 
paid.     How  much  did  the  piano  cost  Wilson? 

26.  I  sold  36%  of  a  purchase  at  15%  profit,  75%  of  the  re- 
mainder at  12%  profit,  and  what  then  remained  at  10%  profit: 
and  gained  $25.52.    What  was  the  amount  of  the  purchase? 

.  21.  An  agent  sold  a  quantity  of  sugar  at  5%  commission  and 


224  NEW  BUSINESS   ARITHMETIC 

invested  the  proceeds  in  corn,  commission  3%  for  buying,  at 
cents  per  bushel.    Find  the  selling  price  of  the  sugar  if  he  bought 
5000  bushels  of  corn. 

28.  An  agent  sold  200  bbls.  of  apples  at  $2  per  bbl.  and 
charged  4%  commission.     He    invested   the   proceeds   after   de- 
ducting 6f%  for  buying,  in  wheat  at  90  cents  per  bu.    How  many 
bushels  did  he  buy? 

29.  A  merchant  sold  J  of  his  stock  at  12%  gain ;  J  of  it  at 
15%  gain;  |  of  it  at  20%  gain;  the  remainder  which  cost  $295 
at  25%.    What  was  his  whole  gain  and  rate  of  gain? 

SO.  A  merchant  bought  40  gallons  of  molasses  at  60  cents  per 
gallon,  and  lost  15%  by  leakage.  At  what  price  per  gallon  must 
he  sell  the  remainder  to  gain  13-J%  on  the  total  cost? 

31.  A  wholesale  merchant  sold  goods  to  Davis  at  40%  profit. 
Davis  failed  and  was  able  to  pay  but  75%  of   his   account.    Did 
the  merchant  gain  or  lose  and  how  much  on  a  bill  of  $1800  ? 

32.  The  price  of  goods  was  marked  down  10%  or  to  $22.50. 
The  dealer  in  order  to  make  a  sale  allowed  another  discount  of 
12%  and  then  sold  at  a  gain  of  23|%.     At  what  %  above  cost 
were  the  goods  marked? 

S3.  A  merchant  bought  6  dozen  pairs  of  gloves  at  $12.90  per 
dozen.  He  sold  2  dozen  at  $1.40  per  pair ;  1|  dozen  at  $1.60  per 
pair;  and  2^  dozen  at  $1.20  per  pair.  What  was  his  gain  %  on 
the  whole  lot? 

34.  Williams  gained  20%   on  his  investment  the  first  year, 
and  25%  the  second  year.     He  lost  10%  the  third  year,  and 
gained  12%  the  fourth  year.    His  capital  was  then  $5292.    How 
much  did  he  invest  ? 

35.  My  agent  sold  a  lot  of  grain  for  me  at  2%  commission, 
and  invested  the  proceeds  in  dry  goods  at  2%  for  buying.    His 
whole  commission  was  $200.    Find  the  cost  of  the  dry  goods  and 
the  selling  price  of  the  grain. 

36.  A  bought  two  houses  for  $1400;  15%  of  the  cost  of  the 
first  was  equal  to  20%  of  the  cost  of  the  second.    He  sold  the  first 
at  13%  profit  and  the  second  at  7f  %  loss.    How   much   did  he 
.gain  by  the  transaction? 


INTEREST 

327.  Interest  is  the  compensation  allowed   for  the  use  of 
money. 

328.  The  Principal  is  the  money  for  the  use  of  which  in- 
terest is  paid. 

329.  The  Amount  is  the  sum  of  principal  and  interest. 

330.  The  Time  is  the  period  during  which  the  principal  bears 
interest. 

331.  The  Rate  of  Interest  is  the  rate  per  cent,  paid  for  one 
year. 

332.  Simple  Interest  is  the  interest  on  the  principal  only. 

333.  Legal  Interest  is  the  interest  or  the  rate  fixed  by  law 
if  no  rate  is  specified  in  the  contract. 

334.  Usury  is  the  interest  at  a  higher  rate  than  allowed  by 
law. 

335.  Common  Interest  is  the  simple  interest  in  which  360 
days  are  considered  a  year;  30  days  a  month;  a  month  T^  of  a 
year. 

This  is  used  in  finding  the  interest  on  notes  and  debts  that 
bear  interest  for  long  periods  of  time — generally  when  the  time 
is  more  than  a  year. 

336.  Bankers  Interest  is  the  simple  interest  in  which  the 
exact  number  of  days  of  each  month  are  reckoned,  and  called 
360ths  of  a  year. 

This  is  used  by  banks,  and  by  business  men  in  finding  the  in- 
terest on  short  time  notes  and  debts. 

337.  Exact  Interest  is  the  simple  interest  in  which  the  exact 
number  of  days  of  each  month  are  reckoned,  and  called  365ths 
of  a  year. 

This  is  used  by  the  U.  S.  Government ;  also  in  finding-  the  in- 
terest on  foreign  money. 

Exact  interest  for  any  time  expressed  in  days  may  be  obtained 
by  subtracting^  from  the  amount  of  common  interest.  Or  common 

15  225 


226 


NEW  BUSINESS   ARITHMETIC 


interest  may  be  obtained  from  exact  interest  by  adding  thereto 
fa  of  the  exact  interest. 

338.  Interest  is  allowed  on  all  notes,  debts  and  contracts 
when  it  is  agreed  upon  by  the  parties ;  on  all  notes,  debts  and 
contracts  after  they  become  due.  When  interest  is  allowed, 
though  no  rate  of  interest  is  expressed,  the  legal  rate  of  the  State 
is  understood. 

The  following  table  shows  the  rates  of  interest  and  penalties  for  usury 
in  the  several  states  and  territories  compiled  from  the  latest  official 
sources.  The  first  column  shows  the  legal  rate  of  interest  when  no  rate 
is  specified ;  the  second  column  shows  the  maximum  rate  allowed  by  law. 


STATES  AND  TERRI- 
TORIES. 

1  LEGAL 
RATE. 

HIGHEST 
RATE 
ALLOWED. 

PENALTY   FOR  USURY. 

Alabama 

8* 

8* 

Forfeiture  of  all  interest. 

Alaska 

8* 

12* 

Arizona 

6* 

any* 

None. 

Arkansas 

6* 

10* 

Forfeiture  of  principal  and  interest. 

California 

1% 

any* 

None. 

Colorado 

8* 

any* 

None. 

Connecticut 

6* 

6* 

None. 

Delaware 

6* 

6* 

Forfeiture  of  double  amount  of  loan. 

Dist.  of  Columbia 

6* 

10* 

Forfeiture  of  all  interest. 

Florida 

8* 

10* 

Forfeiture  of  all  interest. 

Georgia 

1% 

8* 

Forfeiture  of  all  interest. 

Hawaii 

6* 

12* 

Idaho 

1% 

12* 

Forfeiture  of  three  times  the  excess  of  in- 

terest over  12  *. 

Illinois 

5* 

7* 

Forfeiture  of  all  interest. 

Indian  Territory 

6* 

8* 

Indiana 

6* 

8* 

Forfeiture  of  excess  of  interest  over  6  *. 

Iowa 

6* 

8* 

Forfeiture  of  all  interest  and  costs. 

Kansas 

6* 

10* 

Forf.  of  double  the  excess  of  int.  over  In  £. 

Kentucky 

6% 

6* 

Forfeiture  of  excess  of  interest 

Louisiana 

5* 

8* 

Forfeiture  of  all  interest. 

Maine 

6* 

any* 

None. 

Maryland 

6* 

6* 

Forfeiture  of  excess  of  interest. 

Massachusetts 

6* 

any* 

None. 

Michigan 

5* 

7* 

Forfeiture  of  all  interest. 

Minnesota 

6* 

10* 

Forfeiture  of  contract. 

Mississippi 
Missouri 

6* 
6% 

10* 

8* 

Forfeiture  of  interest. 
Forfeiture  of  all  interest. 

Montana 

8$ 

any* 

None. 

Nebraska 

1% 

10* 

Forfeiture  of  all  interests  and  costs. 

Nevada 

1% 

any* 

None. 

New  Hampshire 

6* 

6* 

Forfeiture  of  three  times  the  excess  of  in- 

terest. 

INTEREST 


227 


STATES  AND  TERRI- 
TORIES. 

J 

o 

w 

a 

HIGHEST 
RATE 
ALLOWED. 

PENALTY  FOR  USURY. 

New  Jersey 

6* 

6* 

Forfeiture  of  all  interest  and  costs. 

New  Mexico 

6* 

12* 

None. 

New  York 

6* 

6* 

Forfeiture  of  principal  and  interest. 

North  Carolina 

6* 

6* 

Forfeiture  of  double  the  amount  of  interest. 

North  Dakota 

1% 

12* 

Forfeiture  of  all  interest. 

Ohio 

6* 

8* 

Forfeiture  of  excess  of  interest  over  8  *. 

Oklahoma 

1% 

12* 

Oregon 
Pennsylvania 

6* 
6% 

10* 
6* 

Forfeiture  of  interest,  principal  and  costs. 
Forfeiture  of  excess  of  interest 

Philippine  Islands 

6* 

any  £ 

Porto  Rico 

12* 

12* 

Rhode  Island 

6* 

any* 

None. 

South  Carolina 

1% 

8* 

Forfeiture  of  all  interest. 

South  Dakota 

1% 

12* 

Forfeiture  of  all  interest. 

Tennessee 

6* 

6* 

Forfeiture  of  excess  of  interest. 

Texas 

6* 

10* 

Forfeiture  of  all  interest 

Utah 

8* 

any* 

None. 

Vermont 

6* 

6* 

Forfeiture  of  excess  of  interest. 

Virginia 

6* 

6* 

Forfeiture  of  excess  of  interest  over  8  %. 

Washington 

10* 

12* 

Forfeiture  of  double  illegal  interest. 

West  Virginia 

6* 

6* 

Forfeiture  of  excess  of  interest 

Wisconsin 

6* 

10* 

Forfeiture  of  all  the  interest. 

Wyoming 

8* 

12* 

None. 

Interest  differs  from  other  applications  of  Percentage  in  hav- 
-ing  the  element  of  time  introduced. 

In  computations  in  Interest  five  quantities  are  considered,  viz.  : 
Principal,  Rate,  Time,  Interest  and  Amount. 

In  the  following  problems,  interest  will  mean  common  interest 
unless  otherwise  stated. 

339.  To  find  the  interest  for  any  number  of  years  and 
months. 

ORAL  PROBLEMS 

1.  What  is  the  interest  on  $150  for  1  year  at  3%  ?  at  4%  ?  at 
5%  ?  at  6%  ?  at  ±±%  ? 

2.  What  is  the  interest  for  1  year  at   6%    on   the    following 
amounts  :    $250,  $300,  $40,  $96,  $2000,  $800,  and  $640. 

3.  Find  the  interest  on  $250  for  2  years  at  3<fc,  4%,  5%,  6%. 

4.  Find  the  interest  on  $400  for  1  year  6  months  at  3%, 


5.  What  is  the  interest  on  $600  at  4%  for  1  yr.?  2  yr.?  1  yr.  6 


228  NEW   BUSINESS   ARITHMETIC 

mo.  ?  1  yr.  3  mo.  ?  1  yr.  4  mo.  ?  1  yr.  8  mo.  ?  1  yr.  9  mo.  ?  2  yr.  6 
mo.  ?  2  yr.  2  mo.  ?  2  yr.  8  mo.  ?  3  yr.  ?  3  yr.  9  mo.  ? 

1.  What  is  the  interest  on  $840  for  1  year  9  months  at  6%  ? 

SOLUTION 

1.  1  yr.  9    mo.  =  1J  yr. 

2.  If  X   6%  =  10i9&. 

3.  100%  =  $840.  EXPLANATION.—  Since    1    yr.    9 
/          1  of           e&  /irk  mo-   =   1&   yr-    and   the   rate   for 

one  year  is  6%,  for  Ifc  yr.  - 


,  . 

:  X  6%  =  10#%.    Since  100%  equals 

Or,  $840,   1%  equals  $8.40  and   \W2% 

$840  =  10^  times  $8.40  or  $88.20.     Or 

.06  by  the  second  solution,  the  prin- 


$5CK40  =  interest  for  1  year.    ^  ™ultiplied  by  the  rf  e/qualxs 

$50.40  for  one  year  and   for   \Y4 

.  _  I,  yrs.  the  interest  will  be  1M  times 

37.80  $50.40  or  $88.20. 

50.40 


.20  .=  interest  for  If  years. 
From  this  solution  and  explanation  we  have  the  following : 

To  Find  the  Interest  for  One  or  More  Years 

a.  Let  100%  equal  the  principal. 
\   2).  Find  the  value  of  1%. 

\  c.  Find  the  value  of  the  given  rate  and  this  will  be  the  interest 
for  one  year.  Multiply  this  by  the  number  of  years  and  fractions 
.of  a  year. 

Or,  Multiply  the  principal  by  the  rate  expressed  decimally,  and 
the  result  will  be  the  interest  for  one  year.  Multiply  this  by  the 
number  of  years  and  fractions  of  a  year. 

NOTE. — To  find  the  amount  add  the  interest  to  the  principal. 

Find  the  interest  on : 

2.  $265  for  1  year  at  $%.          5.  $96  for  4  years  at  5%. 

3.  $425.30  for  1  year  at  5%.      6.  $114  for  2  years  at  7%. 

4.  $240  for  3  years  at  6%.         7.  $215  for  5  years  at  8%. 
8.  $120  for  1  yr.  6  mo.  at  12%. 

9_  $320  for  2  yr.  6  mo.  at  5%. 
10.  $160  for  1  yr.  9  mo.  at  6%. 


INTEREST  229 


11.  $248.65  for  4  years  at 

12.  $45  for  6J  years  at  1%. 

13.  $862.50  for  10  years  at 

14.  $1280  for  5  yr.  4  mo.  at  6%. 

15.  Find  the  amount  of  $215  at  6%  for  2  yr.  6  mo. 
NOTE.  —  To  find  the  amount  add  the  interest  to  the  principal. 

16.  Find  the  amount  of  $384.60  at  8%  for  4  yr.  3  mo. 

17.  Find  the  amount  of  $275  at  5%  for  2  yr.  8  mo. 

18.  Find  the  amount  of  $325.60  at  6%  for  2  yr.  9  mo. 

19.  A  merchant  borrowed  $450  for  2  yr.  6  mo.  at  6%.    What 
amount  must  he  pay  at  the  end  of  that  time  ? 

20.  A  loaned  $1268  at  8%  interest  on  May  15,  1903.    What 
amount  will  be  due  August  15,  1905  ? 

21.  I  borrowed  $425.60  on  July  12,  1902,  at  1%  interest.  What 
amount  will  be  due  November  12,  1906? 

22.  On  February  7,  1903,  Amos  Brown  gave  his  note  for  $580' 
bearing  8%  interest.    He  paid  the  note  October  7,  1905.    What 
amount  did  he  pay  ? 

23.  A  loaned  B  $1850  in  Illinois  on  June  16,  1903.     What 
amount  should  B  pay  to  A  in  settlement  February  16,  1905,  no 
rate  being  specified  ? 

24.  A  merchant  in  New  York  gave  his  note  on  September  10, 
1903,  in  payment  for  400  yds.  of  broadcloth  at  $1.50  per  yard. 
What  amount  should  he  pay  in  settlement  June  10,  1905,  no  rate 
being  specified  ? 

25.  A  farmer  sold  his  farm  November  1,  1903,  for  $4500  cash, 
and  loaned  the  amount  at  8%  until  March  1,  1905.     What  did 
the  proceeds  of  the  sale  of  the  farm  amount  to  then  ? 

26.  Andrew  Duncan  loaned  $360  in  Michigan  on  June  20, 
1902,  at  9%.     What  amount  can  he  collect  legally  of  this  debt 
on  October  20,  1905  ? 

340.  To  find  the  interest  on  any  principal  for  months  and 
days. 

1.  Find  the  interest  on  $240  at  6%  for  4  mo.  12  days. 

SOLUTION 

1.  100%  =  $240. 

2.  \%  =  $2.40. 


230  NEW   BUSINESS  ARITHMETIC 

3.  6%  =  $14.40  =  interest  for  1  year. 

4.  $14.40  -T-  12  —  $1.30  =  interest  for  1  mo. 
.-7.  $1.20   X  4  ==  $4.80  =  interest  for  4  mo. 

(t.  $1.20  -f-  30  =  $.04  =  interest  for  1  day. 

7.  $.04  X  12  =  $.48  =  interest  for  12  days. 

,9.  $4.80  +  $.48  =  $5.28  =  interest  for  4  mo.  12  days. 

From  this  solution  and  explanation  we  have  the  rule : 

To  Find  the  Interest  for  Months  and  Days 

a.  Find  the  interest  for  one  year. 

b.  Divide  the  interest  for  one  year  by  12  and  multiply  this  by 
the  given  number  of  mouths. 

c.  Divide  the  interest  for  1  mo.  by  30  and  multiply  by  the  given 
number  of  days. 

d.  Add  the  several  results  together. 

NOTE. — Where  the  months  are  aliquot  parts  of  12,  or  the  days  aliquot 
parts  of  30,  solve  by  the  rule  for  aliquot  parts.  Thus  3  mo.  =  *4  of  a  year; 
10  days  =  Yz  of  a  mo. 

2.  What  is  the  interest  on  $72  at  6%  for  3  months? 

3.  What  is  the  interest  on  $48.50  at  8%  for  4  months? 

4.  What  is  the  interest  on  $150  at  6%  for  6  months? 

5.  What  is  the  interest  on  $240  at  8%  for  7  months? 

6.  What  is  the  interest  on  $275.30  at  6%  for  9  months? 

7.  What  is  the  interest  on  $340  at  6%  for  10  days? 

8.  What  is  the  interest  on  $420  at  7%  for  15  days? 

9.  What  is  the  interest  on  $500  at  8%  for  12  days? 

10.  What  is  the  interest  on  $480  at  6%  for  24  days? 

11.  What  is  the  interest  on  $180  at  8%  for  28  days? 

12.  What  is  the  interest  on  $960  at  6%  for  6  mo.  15  days? 

13.  What  is  the  interest  on  $100.80  at  8%  for  5  mo.  18  days? 

14.  What  is  the  interest  on  $228  at  6%  for  9  mo.  20  days? 

15.  What  is  the  interest  on  $375  at  8%  for  3  mo.  11  days? 

16.  What  is  the  interest  on  $208  at  5%  for  8  mo.  9  days? 

17.  What  is  the  interest  on  $1280  at  4J%  for  T  mo.  1G  days? 

18.  What  is  the  interest  on  $375  at  9%  for  11  mo.  14  days? 

19.  What  is  the  interest  on  $840  at  &%  for  5  mo.  18  days? 

20.  What  is  the  interest  on  $1365  at  8%  for  10  mo.  10  days? 


INTEREST  231 

21.  What  is  the  interest  on  $280  for  2  yr.  2  mo.  2  da.  at  6%  ? 

22.  What  is  the  interest  on  $1620  for  3  yr.  8  mo.  6  da.  at 
7%? 

23.  Find  the  interest  on  $440  for  3  yrs.  6  mo.  at  7%. 

24.  Find  the  interest  on  $400  for  1  yr.  2  mo.  12  days  at  9%. 

25.  Find  the  interest  on  $620  for  1  yr.  6  mo.  24  days  at  4%. 

26.  Find  the  interest  on  $218  for  2  yrs.  9  mo.  18  days  at  8%. 

27.  Find,  the  interest  on  $1250  for  3  yrs.  10  mo.  6  days  at 
10%. 

28.  Find  the  interest  on  $960  for  18  days  at  6%. 

29.  Find  the  interest  on  $260  for  25  days  at  8%. 

30.  Find  the  interest  on  $1080  for  20  days  at  10%. 

31.  Find  the  interest  on  $480  for  15  days  at  9%. 

32.  Find  the  interest  on  $1297.60  for  8  mo.  10  days  at  9%. 

33.  Find  the  interest  on  $1264.80  for  11  mo.  20  days  at  6%. 

34.  Find  the  interest  on  $76.50  for  3  mo.  15  days  at  8%. 

35.  How  much  interest  will  $750  produce  at  11%  from  May 
12,  1900,  to  May  12,  1905? 

36.  I  borrowed  $225  on  October  30,  1902,    at    7%    interest. 
What  amount  of  interest  was  due  October  30,  1905  ? 

87.  On  January  17,  1904,  B  loaned  $248  at  6%  interest.  Find 
the  amount  of  interest  due  on  May  17,  1905. 

38.  $190  was  borrowed  August  21,  1903,  and  the  interest  on 
it  was  paid  May  21,  1905,  at  10%.     Find  the  amount  of  interest. 

39.  Smith  borrowed  $336  on  July  5,  1902,  at    5%    interest. 
He  paid  the  interest  on  same  February  1,  1905.     What  was  the 
amount  of  interest  ? 

40.  On  June  6,  1903  Lyman  gave  his  note  for  $240,  bearing 
10%  interest.  He  paid  the  note  May  21,  1905.     Find  the  amount 
of  interest. 

4-1-  I  accepted  a  note  dated  August  7,  1903,  in  payment  of  a 
lot  sold  for  $744.  The  interest  at  9%  was  paid  October  21,  1905. 
What  amount  of  interest  did  I  receive  ? 

4%.  A  received  a  note  dated  April  3,  1902,  for  $25,  bearing 
4%  interest.  The  maker  of  the  note  paid  the  interest  in  full  on 
November  9,  1905.  Find  the  amount  of  interest  paid. 

43.  A  merchant  sold  goods  amounting  to  $1140  on  January  6, 


232  NEW   BUSINESS   ARITHMETIC 

1905.    He  received  in  payment  a  note  of  same  date,  bearing  12% 
interest.    What  amount  of  interest  is  due  on  March  26,  1905  ? 

44-  Brown  gave  his  note  to  B,  for  borrowed  money,  on  March 
22,  1905.  He  agreed  to  pay  7%  interest  if  the  note  was  paid  in 
less  than  30  days,  and  6%  if  it  was  not  paid  in  that  time.  He 
paid  the  note  April  20.  Find  the  amount  of  interest,  the  prin- 
cipal being  $2450. 

NOTE. — Time  by  compound  subtraction. 

SIXTY  DAYS  METHOD 

341.  To  find  the  interest  at  6%  when  the  time  is  in  days. 
At  6%,  the  interest  is  6  ctsxon  $1  for  1  year  or  12  mo.    There- 
fore the  interest  will  be  Ic  for  2  mo.  or  GO  days. 

ORAL  PROBLEMS 

The  interest  on  $75  for  1  yr.  at  1%  is  $.75. 

The  interest  on  $75  for  6  mo.  at  2%  is  $.75. 

The  interest  on  $75  for  4  mo.  at  3%  is  $.75. 

The  interest  on  $75  for  3  mo.  at  4%  is  $.75. 

The  interest  on  $75  for  2  mo.  (60  da.)  at  6%  is  $.75. 

1.  What  is  the  interest  for  one  year  at  one  per  cent,  on :    $600, 
$750,  $450,  $250,  $375,  $48,  $9,  $28,  $24.36? 

2.  What  is  the  interest  for  2  mo.  at  6%  on:  $200,  $320,  $450, 
$24,  $36,  $84,  $920,  $7? 

3.  What  is  the  interest  on  $720  for  60  days  at   6%?   for    30 
days?  for  20  days?  15  da.?  12  da.?  6  da.?  3  da.? 

4.  What  is  the  interest  on  $6000  for  60  days  at  6%?  59  da.? 
125  da.?  62  da.;  84  da.? 

WRITTEN    PROBLEMS 

1.  Find  the  interest  on  $350  at  6%  for  90  days. 

SOLUTION 

$3.50  =  interest  for  60  days. 
$1.75  =  interest  for  30  days. 
$5.25  =  interest  for  90  days. 

Therefore  we  have  the  following : 


INTEREST  233 

Rule  for  the  Sixty  Days  Method 

a.  Point  off  two  decimal  places  in  the  principal  and  the  result 
be  the  interest  at  6%  for  60  days. 

b.  To  obtain  the  interest  for  a  longer  or  shorter  time  than  60 
days  add  to  or  subtract  from  the  interest  for  60  days. 

c.  To  obtain  the  interest  for  a  greater  or  less  rate  than  6%,  add 
to,  or  subtract  from,  the  result  at  6%. 

Find  the  interest  on  : 

2.  $280  for  60  days  at  6%.    (l2.  $520  for  72  da.  at  5%. 

3.  $530  for  30  da.  at  6%.        13.  $384.25  for  36  da.  at  4f  ?&. 

4.  $480  for  90  days  at  6%.       14-  $250  for  40  da.  at  1$%. 

5.  $780  for  63  da.  at  6%.       15.  $1825  for  6  da.  at  8%. 

6.  $416  for  33  days  at  1%.      16.  $127.30  for  8  da.  at  3%. 

7.  $865.20  for  93  da.  at  5%.  17.  $416.25  for  5  da.  at  o$%. 

8.  $265.50  for  120  da.  at  8%  18.  $580  for  33  da.  at  7%. 

9.  $840  for  75  da.  at  4%.        19.  $184.60  for  36  da.  at  5%. 

10.  $1740  for  45  da.  at  9%.     20.  $465.30  for  27  da.  at  8%. 

11.  $1250  for  48  da.  at  7%. 

SIX  PER  CENT.  METHOD 

342.  To  find  the  interest  at  6%  when  the  time  is  in  years* 
months  or  days. 

The  interest  on  $1  for  1  year  =  .06. 

The  interest  on  $1  for  2  months  =  .01. 

The  interest  on  $1  for  1  month  =  .005.     'J  ^>u^ 

The  interest  on  $1  for  6  days  =  .001.     / 

The  interest  on  $1  for  1  day  =  .000^.  '/0 

1.  What  is  the  interest  on  $120  for  2  yr.  4  mo.  24  da.  at  6%  ? 

SOLUTION 

1.  2  X     $-06     =  $.12  interest  for  2  years. 

2.  4  X  $-005     =     .02  interest  for  4  months. 

3.  24  X  $.000i  =     .004  interest  for  24  days. 

4.  Int.  on  $1         =  $.144 

5.  120  X  $.l-±4    =  $17.28. 

From  the  foregoing  solution  and  explanation  we  have  the 


234  NEW   BUSINESS   ARITHMETIC 

Rule  for  Six  Per  Cent.  Method 

a.  Take  as  many  cents  as  sLv  times  the  years,  one  cent  for  every 
two  months,  one  mill  for  every  six  days  and  one-sixth  of  a  mill  for 
every  additional  day. 

b.  Add  together  these  results  and  we  have  the  interest  upon  $1 
for  the  time  and  rate,  which  multiply  by  the  given  principal. 

c.  To  obtain  the  interest  for  a  greater  or  less  rate  than  6%  add 
to,  or  subtract  from,  the  result  at  6%. 

2.  Find  the  interest  on  $360  for  1  yr.  8  mo.  18  da.  at  6%. 

3.  Find  the  interest  on  $500  for  3  yr.  10  mo.  15  da.  at  6%. 

4.  Find  the  interest  on  $1360  for  4  yr.  7  mo.  24  da.  at  6%. 

5.  Find  the  interest  on  $3200  for  2  yr.  5  mo.  15  da.  at  1%. 

6.  Find  the  interest  on  $1270  for  10  mo.  12  da.  at  8%. 

7.  Find  the  'interest  on  $768  for  5  yr.  4  mo.  7  da.  at  9%. 
S.  Find  the  interest  on  $940  for  11  mo.  27  da.  at  5%. 

9.  Find  the  interest  on  $660  for  9  mo.  9  da.  at  ±%. 

10.  Find  the  interest  on  $475  for  5  mo.  3  da.  at  ty%. 

11.  Find  the  amount  of  $540  for  1  yr.  10  mo.  12  da.  at  8%. 

12.  Find  the  amount  of  $2400  for  24  da.  at  7^%. 

13.  Find  the  amount  of  $1287.40  for  1  mo.  11  da.  at  t'%. 

14.  Find  the  amount  of  $847.80  for  3  mo.  26  da.  at  6$%. 

15.  Find  the  amount  of  $126.10  for  2  mo.  16  da.  at  &%. 

16.  Find  the  amount  of  a  note  for  $218.30  for  2  mo.  20  da. 
at  5-|%. 

17.  Find  the  amount  of  a  note  for  $1625.30  at  7%  for  1  yr.  2 
mo.  18  da. 

IS.  Find  the  amount  of  $735.40  at  10%  interest  for  3  mo. 
25  da. 

19.  Find  the  amount  of  a  note  for  $1420  at  ty%  for  3  >T-  5 
mo.  15  da. 

'20.  Find  the  amount  of  a  note  for  $234.60  at  S$%  for  5  yr.  7 
mo.  4  da. 

21.  Find  the  amount  of  a  note  at  1%  for  $185.60  dated  Oct. 
10,  1903,  and  paid  June  8,  1905. 

22.  S.  B.  Davis  borrowed  $750  on  Aug.  10,  1903,  at  5%  in- 
terest.     He   paid    both    principal    and    interest   June    18,    1905. 
What  amount  did  he  pay  ? 


INTEREST  235 

CANCELLATION  METHOD 

343.   To  find  the  interest  zvhen  the  operation  is  shortened  by 
the  use  of  cancellation. 

1.  Find  the  interest  on  $350  for  9  mo.  at  8%. 

SOLUTION 

350 


.0    .02 

$350   X    3   X    .02  —  $21.00  int. 

We  therefore  have  the  following : 

Rule  for  Cancellation  Method 

a.  Upon  the  right  of  a  perpendicular  line  write  the  principal, 
time  in  months  or  days  and  the  rate. 

b.  If  the  time  is  in  months  place  12  upon  the  left  of  the  line,  or 
if  in  days  place  360  upon  the  left  of  the  line  (unless  the  accurate 
interest  is  required,  in  which  case  place  365). 

c.  Cancel  and  multiply  the  remaining  factors  together  for  the 
required  result. 

NOTE. — The  time  must  be  all  in  months  or  days,  and  not  in  both.   Com- 
mon interest  is  understood  unless  otherwise  stated. 

2.  Find  the  interest  on  $480  at  6%  for  8  mo. 

3.  Find  the  interest  on  $720  at  5%  for  9  mo.  10  da. 

4.  Find  the  interest  on  $1250  at  6%  for  2  yr.  6  mo.  6  da. 

5.  Find  the  interest  on  $160  at  6%  for  1  yr.  9  mo.  18  da. 

I    6.  Find  the  interest  on  $320  at  5%  for  2  yr.  4  mo.  20  da. 
{  7.  Find  the  interest  on  $440  at  7%  for  3  yr.  1  mo.  15  da. 

8.  Find  the  interest  on  $400  at  9%  for  1  yr.  2  mo.  28  da. 

9.  Find  the  interest  on  $750  at  8%  for  11  mo.  16  da. 

10.  Find  the  interest  on  $1264.80  at  6%  for  42  da. 

11.  Find  the  interest  on  $225  at  7%  for  108  da. 

12.  Find  the  interest  on  $1140  at  7%  for  11  mo.  20  da. 

13.  Find  the  amount  of  a  note  for  $1600  drawing  8%  interest 
for  25  da. 

14-  Find  the  amount  of  a  note  for  $1080  at  5%  for  3  mo.  15  da. 
1-1.  A  note  for  $2500  dated  April  3,  1905,  draws  1%  interest 
until  Nov.  19,  1905.    What  will  it  then  amount  to? 


236  NEW   BUSINESS   ARITHMETIC 

COMMON,   BANKER'S  AND   EXACT   INTEREST    COMPARED 

344.  1.  Find  the  common,  banker's  and  exact  interest  on  a 
note  of  $600  at  S%>  dated  January  15,  1905,  and  due  August  24, 
1905. 

COMMON  INTEREST— SIX  PER  CENT.  METHOD 

1905  —  8  —  24. 

1905  —  1  —  15  $6-00  ~  int  for  60  da. 

12.00  =  int.  for  120  da. 

7  —    9-  3.00  =  int.  for  30  da. 

7  mo.  9  da.  -  219  da.  60  =  int  for  6  da. 

NOTE. — In  common  interest  we  -30  —  int.  for  3  da. 

reckon  30  days  as   a  month  and  $21  90  —  int   at  6% 

find  the  time  by   compound  sub-  7  30  =  int   at  2% 

traction.  In  Banker's  and  Exact 
interest  we  find  the  exact  number 
of  days. 

BANKER'S  INTEREST— SIX  PER  CENT.  METHOD 

16  days  in  January.  $6.00  =  int.  for  60  da. 

28  days  in  February.  12.00  =  int.  for  120  da. 

31  days  in  March.  3.00  =  int.  for  30  da. 

30  days  in  April.  1.00  =  int.  for  10  da. 

31  days  in  May.  .10  =  int.  for  1  da. 

30  days  in  June. 

31 'days  in  July.  $22.10  =  int.  at  6%. 

24  days  in  August.  7-36^  =  int.  at  2%. 

221  days.  $29.46^  =  int.  at  8%. 

EXACT  INTEREST 

16  days  in  January. 
28  days  in  February. 

31  days  in  March. 

30  days  in  April. 

31  days  in  May.  221  days  =  f  ft  yr. 

30  days  in  June.  $600  X  yfa  X  IU  =  $29.07. 

31  days  in  July.  $29.07  =  exact  interest. 
24  days  in  August. 

221  days. 

2.  What  is  the  banker's  interest  on  $720  from  May  12,  1904, 
to  January  5,  1905,  at  6%  ? 


INTEREST  237 

3.  What  is  the  exact  interest  on  $365  from  December  10, 
1904,  to  March  15,  1905,  at  6%  ? 

4.  Find  the  difference  between  common  interest  and  banker's 
interest  on  $98.50  from  April  1,  to  October  30,  at  5%. 

5.  Find  the  difference  between  common  interest  and  exact 
interest  on  $210  from  July  23,  to  November  28,  at  10%. 

6.  Find  the  difference  between  banker's  interest  and  exact 
interest  on  $190  from  August  9,  1904,  to  March  16,  1905,  at  6%. 

7.  Find  the  banker's  interest  on  a  note  of  $288  from  January 

4,  to  September  7,  at  10%. 

8.  What  is  the  exact  interest  on  a  note  of  $109.50,  dated  June 
'  7  and  due  December  23,  bearing  5%  interest? 

9.  What  is  the  common  interest  paid  on  a  note  of  $178.25,  at 
8%,  dated  March  1,  1903,  and  due  August  1,  1905? 

10.  What  is  the  difference  between  banker's  interest  and  exact 
interest  on  a  note  of  $1460  bearing  10%,  dated  April  6,  1904,  and 
due  March  9,  1905? 

11.  Which  is  the  greater,  and  how  much  greater,  common  in- 
terest or  banker's  interest  on  a  note  of  $432  from  September  16, 
1904,  to  June  2,  1905,  at  7%? 

12.  Which  is  the  greater,  and  how  much  greater,  common  in- 
terest or  exact  interest  on  a  debt  of  $182.50,  from  July  30,  1904,  to 
April  14,  1905,  at  9%? 

13.  I  borrowed  $2555  at  exact  interest  and  loaned  same  at 
banker's  interest.    Did  I  gain  or  lose,  and  how  much  from  May 

5,  to  November  22,  interest  at  7$%  ? 

14-  Would  I  gain  or  lose  and  how  much,  to  borrow  $32850  at 
8%,  at  common  interest  and  loan  it  at  exact  interest  from  De- 
cember 28,  1904,  to  July  13,  1905? 

15.  How  much  is  gained,  money  worth  6J%,  by  borrowing 
$4800  at  common,  interest  and  loaning  it  at  banker's  interest  from 
July  23,  1904,  to  June  26,  1905? 

16.  Find  the  interest  on  7  U.  S.  bonds  of  $1000  each  from 
November  6  to  March  28,  at  4J% 

NOTE.— Exact  interest  is  used  in  computing  interest  on  U.  S.  securities 
and  foreign  money. 


238  NEW   BUSINESS   ARITHMETIC 

17.  Find  the  interest  on  a  $500  U.  S.  bond,  bearing  ±\%  inter- 
est from  April  1  to  July  25. 

IS.  What  is  the  interest  on  £240  9s.  3d.  for  90  days  at  8%? 

NOTE. — Reduce  shilling  and  pence  to  decimal  of  a  pound,  then  find  the 
interest  as  in  U.  S.  money,  after  which  reduce  the  decimal  of  pounds  back 
to  lower  denominations. 

19.  What  is  the  interest  on  £920  7s.  6d.  from  February  5  to 
July  1,  at  56/0? 

20.  Find  the  interest  on  £1335  11s.  3d.  at  4%,  from  March  4 
to  October  10. 

21.  Find  the  interest  on  a  note  of  £270  12s.  at  7%,   from 
April  10  to  September  3. 

22.  Find  the  interest  on  a  note  of  £120  15s.  at  6%,  for  146 
days. 

gS.  Find  the  interest  on  £1999  8s.  9d.  from  July  8,  1905  to 
Oct.  24,  1907  at  10%. 

PROBLEMS  IN  INTEREST 

345.  To  find  the  time,  ivhcn  the  principal,  rate  and  interest 
or  amount  are  given. 

1.  I  received  $9  interest  on  $150  loaned  at  4%.  For  how 
long  was  the  money  loaned  ? 

SOLUTION 

$150 
.04 


$6.00  =  interest  for  1  yr. 

$9  -j-  $6  =  1J  or  1  yr.  6  mo. 

From  this  solution  we  have  the  following: 
To  Find  the  Time 

a.  Find  the  interest  on  the  principal  for  one  year. 

b.  Divide  the  given  interest  by  the  interest  for  one  year  and 
the  result  will  be  the  time  in  years. 

2.  In  what  time  will  $280  produce  $49  interest  at  7%  ? 

3.  In  what  time  will  $160  produce  $15.36  interest  at  8%  ? 

4.  In  what  time  will  $225  produce  $72.90  interest  at  9%  ? 


INTEREST  239 

5.  In  what  time  will  $618.50    produce    $25.14    interest   at 
6%? 

6.  In  what  time  will  $750  produce  $2.25  interest  at  4%  ? 

7.  I  received  $33  interest  on  a  loan  of  $300  at  o%.    For  how 
long  was  the  money  loaned? 

S.  A  farmer  borrowed  $640  at  9%  on  June  1,  1904,  and  paid 
$801.28  for  the  note  and  interest  at  maturity.  Find  the  maturity 
of  the  note. 

9.  On  July  16,  1905,  I  paid  $860.36  for  a  note  of  $785,  bear- 
ing 12%  interest.  Find  the  date  of  the  note. 

10.  What  is  the  date  of  a  note  bearing  11%  interest  for  $190 
on  which  $52.25  interest  was  (lue  May  30,  1905? 

11.  I  borrowed  $335  on   February  4,   1905,  and   found  the 
amount  at  maturity  to  be  $452.92.     When  will  the  note  mature, 
it  bearing  8%   interest? 

12.  On  August  24,  1905,  I  borrowed  $600  on  my  note  at  ±\% 
interest  and  at  maturity  paid  $621  for  note  and  interest.     Find 
the  date  of  maturity,  allowing  banker's  interest. 

346.  To  find  the  rate,  when  the  principal  or  amount,  interest 
and  time  are  given. 

1.  At  what  rate  of  interest  will  $500  in  1  yr.  8  mo.  24  da. 
produce  $52? 

SOLUTION 

$5.00     =  int.  1  yr.  \%. 

2.50     =  int.  6  mo. 

.83J  =  int.  2  mo. 

.2;i  =  =  int.  20  da. 

.05     =  int.  4  da. 

$8.60 J  =  int.  at  \%. 

$52  -r-  $8.66§  =  6  ==  6%. 

From  this  solution  and  explanation  we  have  the  following: 
To  Find  the  Rate 

a.  Find  the  interest  on  the  principal  at  1%  for  the  given  time. 

b.  Divide  the  given  interest  by  the  interest  at  1%,  ana  the  re- 
sult will  be  the  rate. 


240  NEW  BUSINESS   ARITHMETIC 

NOTE. — If  the  amount  is  given,  subtract  the  principal  from  it  to  find 
the  interest. 

2.  At  what  rate  of  interest  will  $720  produce  $172.80  in  2 
yrs.  ? 

S.  At  what  rate  of  interest  will  $480  produce  $84  in  2  yrs. 

6  mo.? 

4.  At  what  rate  of  interest  will  $320  produce  $48.96  in  3  yrs. 

9  mo.  27  days? 

5.  At  what  rate  of  interest  will  $1275  produce  $242.25  in  1  yr. 

10  mo.  24  days  ? 

6.  At  what  rate  of  interest  will  $85  produce  $43.01  in  4  yrs. 

7  mo.  6  days? 

7.  A  paid  $36  interest  on  a  note  of  $240,  that  had  been  on 
interest  for  1  yr.  8  mo.    Find  the  rate  of  interest. 

8.  I  loaned  Smith  $900  for  2  yrs.  8  mo.  12  days,  and  at  the 
end  of  that  time  he  paid  me  $1094.40  in  full  for  his  note  and  in- 
terest.   What  rate  of  interest  did  the  note  draw  ? 

9.  A  merchant  received  from  Brown  $218.96  for  his  note  of 
$170  that  had  been  at  interest  for  3  yrs.  7    mo.    6    days.     What 
rate  of  interest  was  charged? 

10.  Snyder  borrowed  on  his  note  $97.50  for  1  yr.  7  mo.  18 
days.     He  paid  $6  interest  at  the  end  of  the  year,  and  at  matur- 
ity found  the  sum  due  was  $101.055.    Find  the  rate  of  interest. 

11.  On  January  6  I  loaned  $144,  and  on  December    31    re- 
ceived the  amount  due,  which  was  $158.20.     What  rate  of  inter- 
est did  I  charge? 

12.  B  borrowed  $45  on  October  30,  1905,  and  paid  the  note 
and  interest  with  $47.39  on  June  29,  1906.     Find  the  rate  of  in- 
terest he  paid. 

347.  To  find  the  principal,  when  the  interest,  rate  and  time 
are  given. 

1.  I  received  $226  interest  on  a  sum  loaned  for  1  yr.  4  mo.  at 
6.    How  much  was  the  loan? 


INTEREST  241 

SOLUTION 

$.06  =  int.  on  $1  for  1  yr. 
.02  =  int.  on  $1  for  4  mo. 
$.08  =  int.  on  $1  for  the  given  time 

and  rate. 

$226  -7-  .08=  $2825  =  the  principal. 
From  the  foregoing  we  have  the  following: 

To  Find  the  Principal 

a.  Find  the  interest  on  $1  for  the  given  time  at  the  given  rate. 

b.  Divide  the  given  interest  by  the  interest  on  $1,  and  the  quo- 
tient will  be  the  required  principal. 

2.  What  principal  will  produce  $62.50  interest  in  2  yrs.  6 
mo.  at  5%? 

3.  What  principal  will  produce  $39.78  interest  in  1  yr.  4  mo. 
18  days  at  9%  ? 

4.  What  principal  will  produce  $63.22  interest  in  3  yrs.  7  mo. 
15  days  at  8%  ? 

5.  What  principal  will  produce  $11.22  interest  in  9  mo.  27 
days  at  10%  ? 

6.  What  principal  will  produce  $20.235  interest  in  4  mo.  20 
days  at  12%? 

7.  B  paid  me  $154.47  interest  on  a  note  bearing  9%.    What 
was  the  principal  if  the  note  was  for  2  yrs.  3  mo.  3  days  ? 

8.  James  Irwin  received  $10.97  interest  on  a  note  bearing  7% 
interest.    The  note  was  dated  January  6,  1905,  and  paid  July  12, 
1906.    Find  the  principal. 

9.  The  interest  on  a  note  bearing   6%,    dated    October    14, 
1905,  and  paid  August  10,  1906,  was  $39.43^.     Find  the  princi- 
pal. 

10.  I  paid  $420  for  a  stock  of  goods  and  sold  same  to  B  on 
his  note  for  2  yrs.  6  mo.  at  6%  interest.    The  interest  on  the  note 
was  $71.19.    At  what  %  profit  did  I  sell  the  goods? 

11.  William  Graham  borrowed  money  on  his  note  at  4%  for 
3  yrs.  8  mo.  12  days.    He  invested  the  sum  borrowed  in  potatoes 
at  25  cents  per  bushel.    How  many  bushels  did  he  buy,  if  the  in- 
terest for  the  time  was  $18.50? 

16 


242  NEW   BUSINESS   ARITHMETIC 

348.  To  find  the  principal  zvhen  the  amount,  rate  and  time 
are  given. 

1.  What  principal  in  2  yrs.  1  mo.  15  days  at  8%  interest  will 
amount  to  $421.20? 

SOLUTION 

$.17  =  int.  on  $1  for  the  given 

time  and  rate. 
1.00 


$1.17  =  amount  of  $1.     . 
$421.20  -f-  1.17  =  $360  principal. 

2.  What  principal  in  3  yrs.  9  mo.  21  days  at  1%  interest  will 
amount  to  $303.98  ? 

3.  What  principal  in  5  yrs.  7  mo.  28  days  at  9%  interest  will 
amount  to  $558.51|  ? 

4-  What  principal  in.  11  mo.  10  days  at  10%  interest  will 
amount  to  $1280.50? 

5.  What  principal  in  5  mo.  12  days  at  5%  interest  will  amount 
to  $184.05  ? 

6.  I  owe  $780,  due  in  2  yrs.  6  mo.     What  sum  will  pay  it 
now,  if  money  is  worth  8%  interest? 

7.  A  note  bearing  7%  interest,  having  run  for  1  yr.  2  mo.  12 
days,  was  paid  with  $596.20.    Find  the  principcu    <* 

8.  Adams  paid  $2592.60  for  his  note  that  had  been  on  inter- 
est for  2  yrs.  4  mo.  24  days  at  8%.    What  was  the  principal  of 
the  note  ? 

9.  What  sum  is  required  to  pay  a  debt  of  $125.78,  due  in  .°> 
yrs.  7  mo.  6  days,  if  interest  is  allowed  at  9%  ? 

10.  West  borrowed  $296.01  to  pay  a  note  that  had  been  on 
interest  at  4%  for  10  mo.  15  days.  Find  the  sum  for  which  the 
note  was  given. 

11  I  bought  goods  to  the  amount  of  $757.12  on  4  mo.  24 
days  time.  I  borrowed  money  and  paid  cash  for  the  goods.  How 
much  did  I  borrow  if  10%  interest  was  allowed? 


INTEREST  243 

ANNUAL  INTEREST 

349.  Annual  Interest  is  interest  payable  annually  or  at  other 
regular  intervals  of  time. 

350.  If  the  Annual  Interest  is  not  paid  when  due,  it  draws 
simple  interest  from  the  time  it  becomes  due  until  it  is  paid. 

Annual  interest  is  legalized  in  Michigan  at  the  same  rate  as  secured  by 
the  contract ;  in  Ohio,  Wisconsin,  Vermont,  New  Hampshire,  and  Iowa, 
at  6%;  and  in  Pennsylvania,  Georgia,  Illinois  and  Indiana,  by  special  con- 
tract only. 

When  notes  are  made  to  run  for  a  term  of  years  secured  by 
real  estate  or  collaterals,  it  is  customary  to  represent  the  principal 
by  one  or  more  "Principal  notes"  which  do  not  read  to  draw  in- 
terest, and  then  the  several  payments  of  interest  are  evidenced  by 
interest  notes  maturing  at  the  time  each  interest  payment  is  pay- 
able. These  interest  notes  as  well  as  the  principal  notes  are  en- 
titled to  draw  interest  after  maturity,  like  any  other  note. 

1.  What  is  due  on  a  note  of  $300  at  6%  for  five  years,  inter- 
est payable  annually,  no  payment  having  been  made  until  the 
maturity  of  the  note  ? 

SOLUTION 
.  $300 
.06 


>.00  =^nt.  for  1  yr. 

_5 

).00  int.  for  5  yr. 
4  yr.  +  3  yr.  +  2  yr.  +  1  yr.  =  10  yr. 
Int.  on  $18  for  10  yr.  =  $10.80. 
$300  +  $90  +  $10.80  =  $400.80. 
From  the  foregoing  solution  we  have  the  following: 

To  Find  the  Annual  Interest 

a.  Find  the  interest  on  the  principal  until  the  time  of  settle- 
ment. 

b.  Find  the  interest  upon  the  first  year's  interest  for  the  sum 
of  the  times  ivhich  the  several  payments  of  interest  have  to  run 
until  maturity. 

c.  Add  together  the  principal,  the  interest  thereon,  and  the  in- 


244  NEW   BUSINESS   ARITHMETIC 

terest  due  on  each  year's  interest.    The  result  will  be  the  'amount 
due  at  maturity. 

NOTE. — In  case  the  interest  is  payable  semi-annually  or  quarterly  it  is 
computed  in  the  same  manner  as  annually,  substituting  a  half  or  quarter 
year  for  year. 

2.  Find  amount  due  on  a  note  of  $800  for  1  yr.  8  mo.  12  days 
at  8%,  interest  payable  quarterly,  no  payments  being  made  be- 
fore maturity  of  the  note. 

NOTE. — At  the  expiration  of  each  quarter,  $16  is  due.  The  first  quarter's 
interest  bears  interest  for  1  yr.  5  mo.  12  days;  the  second  quarter's,  for  1 
yr.  2  mo.  12  days,  etc. 

Find  the  amount  due  on  the  following  notes,  no  payments  hav- 
ing been  made  before  maturity  of  the  note. 

3.  $350  for  3  years  at  7%,  interest  payable  annually. 

4.  $910  for  3  yrs.  7  mo.  15  days  at  10%,  interest  payable  an- 
nually. 

5.  $460  for  2  years  at  5%,  interest  payable  semi-annually. 

6.  $590  for  1  yr.  11  mo.  12  days  at  8%,  interest  payable  semi- 
annually. 

Find  the  amount  due  on  the  following  notes,  no  payments  hav- 
ing been  made : 

7.  $1290  for  1  year  at  4%,  interest  payable  quarterly. 

8.  $180  for  1  yr.  9  mo.  18  days  at  10%,  interest  payable  quar- 
terly. 

9.  What  is  the  interest  on  a  debt  of  $680  due  in  3  yrs.  4  mo. 
18  da.  at  1%  interest  payable  annually  and  no  payments  having 
been  made  ? 

10.  On  August  16,  1902,  A  loaned  $3465  at  5%,  interest  pay- 
able quarterly.     If  no  payments  have  been  made,  what  amount 
was  due  January  1,  1904? 

11.  A  farmer  borrowed  $1250  on  June  1,  1903,  and  gave  his 
note  drawing  6%  interest  payable    semi-annually.     If    no    pay- 
ments have  been  made,  what  will  be  the  amount  of  the  note  April 
13,  1905? 


INTEREST  245 

COMPOUND  INTEREST 

351.  Compound  Interest  is  the  interest  on  the  principal  and 
its  unpaid  interest  added  to  it  at  the  end  of  each  period  of  time 
for  which  the  interest  is  made  payable. 

352.  Interest  may  be  compounded  according  to  agreement, 
at  the  end  of  each  year,  half  year  or  any  other  period  of  time. 

Compound  interest  cannot  be  enforced  by  law  in  most  of  the 
states,  but  if  the  debtor  is  willing  to  pay  compound  interest  he 
may  do  so  without  violating  the  law  against  usury. 

1.  What  is  the  compound  interest  on  $300  at  8%  for  three 
years,  interest  compounded  annually? 

SOLUTION 

1.  $300  X   .08  =  $24,  interest  first  year. 

2.  $300  +  $24  =  $324,  principal  second  year. 

3.  $324  X   -08  =  $25.92,  interest  second  year. 

4.  $324  +  $25.92  =  $349.92,  principal  third  year. 

5.  $349.92  X    .08  =  $27.994,  interest  third  year. 

6.  $349.92  +  $27.994  =  $377.914,  amount  due. 

7.  $377.914  --  $300  =  $77.914,  the  compound  interest. 

From  this  solution  and  explanation  we  have  the  following : 

To  Find  the  Compound  Interest 

a.  Find  the  amount  of  the  principal  for  one  year  and  make  this 
the  principal  for  the  second  year. 

b.  Find  the  amount  of  this  new  principal  for  the  second  year 
and  make  it  the  principal  for  the  third  year,  etc. 

c.  Subtract  the  original  principal  from  the  last  amount  and 
the  result  will  be  the  compound  interest. 

NOTES. — 1.  When  the  interest  is  payable  semi-annually  or  quarterly, 
find  the  amount  of  the  given  principal  for  the  first  interval,  and  make  it 
the  principal  for  the  second  interval,  proceeding  in  all  respects  as  when  the 
interest  is  payable  yearly. 

2.  When  the  time  contains  years,  months  and  days,  find  the  amount 
for  the  even  intervals  upon  which  compute  the  interest  for  the  remaining 
months  and  days,  and  add  it  to  the  last  amount,  before  subtracting. 


246  NEW   BUSINESS   ARITHMETIC 

Find  the  compound  interest  of 

2.  $600  for  4  years  at  5%,  interest  compounded  annually. 

3.  $720  for  3  years  at  9%,  interest  compounded  annually. 

4.  $1800  for  4  yrs.   8  mo.   12  days  at  10%,  interest  com- 
pounded annually.  (  O  I  ^  tf&  }  »"4 .  \ 

5.  $860   for  2  years  at  S%,  interest  compounded  semi-an- 
nually. 

6.  $2700  for  2  yrs.  4  mo.  at  6%,  interest  compounded  semi- 
annually. 

7.  $3350  for  3  yrs.  2  mo.  20  days  at    10%,    interest    com- 
Bounded  semi-annually. 

8.  $180  for  1  year  at  5%,  interest  compounded  quarterly. 

9.  $450  for  1  yr.  1  mo.  at  1%,  interest  compounded  quarterly. 
10.  $920  for  1  yr.  7  mo.  24  days  at  &%,  interest  compounded 

quarterly. 

Where  the  time  is  long,  the  labor  of  computing  compound  in- 
terest may  be  greatly  shortened  by  using  the  table. 

To  find  the  compound  amount  of  $1  by  the  table  look  in  the  column 
at  the  left  of  the  page  for  the  years  and  under  the  given  rate  per  cent,  at 
the  top  of  the  page. 

If  the  interest  is  compounded  semi-annually,  it  is  equivalent  to  double 
the  number  of  years  at  half  the  rate  per  cent,  or  quarterly,  four  times  the 
years  at  one-fourth  the  rate. 

The  amount  of  $1  as  found  by  the  table,  multiplied  by  the  given  prin- 
cipal will  give  the  compound  amount  of  the  principal. 

The  labor  of  computing  compound  interest  may  be  greatly 
shortened  by  the  use  of  the  following : 


INTEREST 

Compound  Interest  Table 


247 


Showing  the  amount  of  $1  at  compound  interest  at  various 
^s  per  cent,  for  any  number  of  years,  from  1  year  to  50  years, 


rates  per 
inclusive. 


Years. 

1  per  ct. 

VA  perct. 

2  per  ct. 

2%  per  ct. 

3  per  ct. 

3',  per  ct. 

4  per  ct. 

1 
2 
3 

4 

1.0100000 
1.0201  000 
1.0303  010 
1.0406040 
1.0510  101 

1.0150000 
1.0302  250 
1.0456  7S4 
1.0613  636 
1.0772  840 

1.02000000 
1.04040000 
1.0612  0800 
1.0824  3216 
1.10408080 

1.0250  0000 
1.0506  2500 
1.07689062 
1.1038  1289 
1.13140821 

1.0300  0000 
1.06090000 
1.0927  2700 
1.1255  0881 
1.1592  7407 

1.0350  0000 
1.0712  2500 
.1087  1787 
.1475  2300 
.1876  8631 

1.04000000 
1.08160000 
1.1248  6400 
1.16985856 
1.2166  5290 

6 
7 
8 
9 
10 

1.0615  202 
1.0721  354 
1.0828567 
1.0936  853 
1.1046221 

1.0934433 
1.1098  450 
1.1264  926 
1.1433  900 
1.1605  408 

1.1261  6242 
1.14868567 
1.1716  5938 
1.19509257 
1.2189  9442 

.15969342 
.1886  8575 
.2184  0290 
.2488  6297 
.28008454 

1.1940  5230 
1.2298  7387 
1.2667  7008 
1.3047  7318 
1.3439  1638 

.2292  5533 
.2722  7926 
.3168  0904 
.3628  9735  , 
1.4105  9876 

1.2653  1902 
1.3159  3178 
1.3685  6905 
1.4233  1181 
1.4802  4428 

11 
12 
13 
14 
15 

.1156683 
.1268  250 
.1380  933 
.1494  742 
.1609690 

1.1779  489 
1.1956  182 
1.2135  524 
1.2317  557 
1.2502  321 

1.2433  7431 
1.26824179 
1.29360663 
1.3194  7876 
1.3458  6834 

1.31208666 
1.34488882 
1.3785  1104 
1.4129  7382 
1.4482  9817 

1.3842  3387 
1.4257  6089 
1.4685  3371 
1.5125  8972 
1.5579  6742 

1.4599  6972 
1.51106866 
1.5639  5606 
1.61869452 
1.6753  4883 

1.5394  5406 
1.6010  3222 
1.6650  7351 
1.7316  7645 
1.8009  4351 

16 
17 
18 
19 
20 

.1725  786 
.1843044 
.1961  475 
.2081090 
.2201900 

1.2689855 
1.2880203 
1.3073  406 
1.3269  507 
1.3468  550 

1.37278570 
1.40024142 
1.4282  4625 
1.4568  1117 
1.4859  4740 

1.4845  0562 
.5216  1826 
.5596  5872 
.5986  5019 
.63861644 

1.60470644 
1.65284763 
1.7024  3306 
1.7535  0605 
1.8061  1123 

1.73398601 
1.7946  7555 
1.8574  8920  j 
1.9225  0132  ! 
1.9897  8886 

1.8729  8125 
1.9479  0050 
2.0258  1652 
2.1068  4918 
2.1911  2314 

21 
22 
23 
24 
25 

.2323  919 
.2447  159 
.2571  630 
.2697  346 
.2824  320 

1.3670  578 
1.3875  637 
1.4083  772 
1.4295028 
1.4509  454 

1.51566634 
1.5459  7967 
1.57689926 
1.60843725 
1.6406  0599 

.6795  8185 
.7215  7140 
.76461068 
1.8087  2595 
1.85394410 

1.8602  9457 
1.9161  0341 
1.9735  8651 
2.03279411 
2.0937  7793 

2.0594  3147 
2.1315  1158 
2.2061  1448 
2.2833  2849 
2.3632  4498 

2.2787  CS07 
2.3699  1879 
2.4647  1555 
2.5633  0417 
2.6658  3633 

26 
27 
28 
29 
30 

.2952  563 
.3082  089 
.3212  910 
.3345  039 
.3478  490 

1.4727  095 
1.4948  002 
1.5172222 
1.5399  805 
1.5630  802 

1.6734  1811 
1.70688648 
1.7410  2421 
1.7758  4469 
1.8113  6158 

1.9002  9270 
1.94780002 
1.99649502 
2.0464  0739 
2.0975  6758 

2.1565  9127 
2.2212  8901 
2.2879  2768 
2.3565  6551 
2.4272  6247 

2.4459  5856 
2.5315  6711 
2.6201  7196 
2.7118  7798 
2.8067  9370 

2.7724  6979 
2.8833  t858 
2.9987  0332 
3.11865145 
3.2433  9751 

31 
32 
33 
34 
35 

.3613  274 
.3749  407 
.3886  901 
.4025  770 
.4166  028 

1.5865  264 
.6103  243 
.6344  792 
.6589  964 
.6838813 

1.8475  8882 
1.8845  4059 
1.92223140 
1.96067603 
1.9998  8955 

2.1500  0677 
2.2037  5694 
2.2588  5086 
2.3153  2213 
2.3732  0519 

2.5000  8035 
2.5750  8276 
2.6523  3524 
2.7319  0530 
2.8138  6245 

2.9050  3148 
3.0067  0759 
3.11194235 
3.2208  6033 
3.3335  9045 

3.3731  3341 
3.5080  5875 
3.64838110 
3.7943  1634 
3.9460  8899 

36 
37 
38 
39 
40 

.4307  688 
.4450  765 
.4595  272 
.4741  225 
.4888637 

.7091  395 
.7347  766 
.7607983 
.7872  103 
.8140  184 

2.0398  8734 
2.0806  8509 
2.12229879 
2.16474477 
2.2080  3966 

2.4325  3532 
2.4933  4870 
2.5556  8242 
2.6195  7448 
2.6850  6384 

2.8982  7833 
2.9852  2668 
3.0747  8348 
3.1670  2698 
3.2620  3779 

3.4502  6611 
3.5710  2543 
3.6960  1132 
3.8253  7171 
3.9592  5972 

4.1039  3255 
4.2680  8986 
4.4388  1345 
4.6163  6599 
4.8010  2063 

41 
42 
43 
44 
45 

.5037  524 
.5187  899 
.5339  778 
.5493  176 
.5648  107 

.8412  287 
.8688471 
.8968  798 
.9253  330 
.954  J  130 

2.7521  9043 
2.8209  9520 
2.8915  2008 
2.9638  0808 
3.0379  0328 

3.3598  9893 
3.4606  9589 
3.5645  1677 
3.6714  5227 
3.7815  9584 

4.0978  3381 
4.2412  5799 
4.3897  0202 
4.5433  4160 
4.7023  5855 

4.9930  6145 
5.1927  8391 
5.4004  9527 
5.6165  1508 
5.8411  7568 

46 
47 
48 
49 
50 

.5804  589 
.5962634 
.6122  261 
.6283483 
.6446318 

1.9835  262 
2.0132  791 
2.0434  783 
2.0741  305 
2.1052424 

2.4866  1129 
2.5363  4351 
2.5870  7039 
2.6388  1179 
2.6915  8803 

3.1138  5086 
3.19169713 
3.2714  8956 
3.3532  7680 
3.4371  0872 

3.8950  4372 
4.01189503 
4.1322  5188 
4.2562  1944 
4.3839  0602 

4.8669  4110 
5.03728404 
5.2135  8898 
5.3960  6459 
5.5849  2686 

6.0748  2271 
6.3178  1562 
6.5705  2824 
6.8333  4937 
7.1066  8335 

248 


NEW   BUSINESS   ARITHMETIC 


Compound  Interest  Table 

Showing  the  amount  of  $1  at  compound  interest  at  various 
rates  per  cent,  for  any  number  of  years,  from  1  year  to  50  years, 
inclusive. 


Years. 

V/2  per  ct. 

5  per  ct. 

6  per  ct. 

7  por  ct. 

8  per  ct. 

9  per  ct. 

10  per  ct. 

1 
2 
3 

5 

1.0450  0000 
1.0920  2500 
1.14116612 
1.1925  1860 
1.2461  8194 

1.0500  000 
.1025  000 
.1576250 
.2155  063 
.2762  816 

1.0600000 
.1236  000 
.1910  160 
.2624  770 
.3382  256 

1.0700  000 
.1449  000 
.2250  430 
.3107  960 
.4025  517 

.0800  000 
.1664000 
.2597  120 
.3604  890 
.4693  281 

.0900  000 
.1881  000 
.2950  290 
.4115  816 
.5386  240 

1.1000  000 
1.2100  000 
1.3310  000 
1.4641000 
1.6105  100 

6 
7 
8 

10 

1.3022  6012 
1.3608  6183 
1.4221  0061 
1.4860  9514 
1.5529  6942 

.3400956 
.4071  004 
.4774  554 
.5513  282 
.6288  946 

.4185  191 
.5036  303 
.5938  481 
.6894  790 
.7908  477 

.5007  304 
.6057  815 
.7181  862 
.8384  592 
.9671  514 

.5668  743 
.7138  243 
.8509  302 
.9990  046 
2.1589  250 

1.6771  001 
1.8280  391 
1.9925  626 
2.1718933 
2.3673  637 

1.7715  610 
1.9487  171 
2.1435  888 
2.3579  477 
2.5937  425 

11 
12 
13 
14 
15 

1.6228  5305 
1.69588143 
1.7721  9610 
1.8519  4492 
1.9352  8244 

.7103  394 
.7958  563 
.8856  491 
.9799  316 
2.0789  282 

1.8982986 
2.0121  965 
2.1329  283 
2.2609  040 
2.3965  582 

2.1048  520 
2.2521  916 
2.4098  450 
2.5785  342 
2.7590  315 

2.3316  390 
2.5181  701 
2.7196  237 
2.9371  936 
3.1721  691 

2.5804  264 
2.8126  648 
3.0658  046 
3.3417  270 
3.6424  825 

2.8531  167 
3.1384  284 
3.4522  712 
3.7974  983 
4.1772  482 

16 
17 
18 
19 
20 

2.0223  7015 
2.1133  7681 
2.2084  7877 
2.3078  6031 
2.4117  1402 

2.1828  746 
2.2920  183 
2.4066  192 
2.5269  502 
2.6532  977 

2.5403  517 
2.6927  728 
2.8543  392 
3.0255  995 
3.2071  355 

2.9521  638 
3.1588  152 
3.3799  323 
3.6165  275 
3.8696  845 

3.4259  426 
3.7000  181 
3.9960  195 
4.3157011 
4.6609  571 

3.9703  059 
4.3276  334 
4.7171  204 
5.1416613 
5.6044  108 

4.5949  730 
5.0544  703 
5.5599  173 
6.1159  390 
6.7275  000 

21 
22 
23 
24 
25 

2.52024116 
2.6336  5201 
2.7521  6635 
2.8760  1383 
3.0054  3446 

2.7859  626 
2.9252  607 
3.0715  238 
3.2250  999 
3.3863  549 

3.3995  636 
3.6035  374 
3.8197  497 
4.0489  346 
4.2918  707 

4.1405  624 
4.4304  017 
4.7405  299 
5.0723  670 
5.4274  326 

5.0338  337 
5.4365  404 
5.8714  637 
6.3411  807 
6.8484  752 

6.1088  077 
6.6586  004 
7.2578  745 
7.9110  832 
8.6230  807 

7.4002  499 
8.1402  749 
8.9543  024 
9.8497  327 
10.8347  059 

26 
27 
28 
29 
30 

3.1406  7901 
3.2820  0956 
3.4296  9999 
3.5840  3649 
3.7453  1813 

3.5556  727 
3.7334  563 
3.9201  291 
4.1161  356 
4.3219  424 

4.5493  830 
4.8223  459 
5.1116867 
5.4183  879 
5.7434  912 

5.8073  529 
6.2138  676 
6.6488  384 
7.1142  571 
7.6122  550 

7.3963  532 
7.9880  615 
8.6271  064 
9.3172  749 
10.0626  569 

9.3991  579 
10.2450  821 
11.1671  395 
12.1721  821 
13.2676  785 

11.9181  765 

13.1099  942 
14.4209  936 
15.8630  930 
17.4494  023 

31 
32 
33 
34 
35 

3.9138  5745 
4.0899  8104 
4.2740  3018 
4.4663  6154 
4.6673  4781 

6.0881  006 
6.4533  867 
6.8405  899 
7.2510  253 
7.6860  868 

8.1451  129 
8.7152  708 
9.3253  398 
9.9781  135 
10.6765  815 

10.8676  694 
11.7370830 
12.6760  496 
13.6901  336 
14.7853  443 

14.4617  695 
15.7633  288 
17.1820  284 
18.7284  109 
20.4139  679 

19.1943  425 
21.1137  768 
23.2251  544 
25.5476  699 
28.1024  369 

36 
37 
38 
39 
40 

4.8773  7846 
5.0968  6049 
5.3262  1921 
5.5658  9908 
5.8163  6454 

5.7918  161 
6.0814  069 
6.3854  773 
6.7047  512 
7.0399  887 

8.1472  520 
8.6360  871 
9.1542  524 
9.7035  075 
10.2857  179 

11.4239422 
12.2236  181 
13.0792  714 
13.9948  204 
14.9744  578 

15.9681  718 
17.2456256 
18.6252  756 
20.1152977 
21.7245  215 

22.2512  250 
24.2538  353 
26.4366  805 
28.8159  817 
31.4094  200 

30.9126  805 
34.0039  486 
37.4043  434 
41.1447  778 
45.2592  556 

41 
42 
43 
44 
45 

6.0781  0094 
6.3516  1548 
6.6374  3818 
6.9361  2290 
7.2482  4843 

7.3919  882 
7.7615  876 
8.1496669 
8.5571  503 
8.9850  078 

10.9028  610 
11.5570327 
12.2504  546 
12.9854  819 
13.7646  108 

16.0226  699 
17.1442  568 
18  3443  548 
19.6284  596 
21.0024  518 

23.4624  832 
25.3394  819 
27.3666  404 
29.5559  717 
31.9204  494 

34.2362  679 
37.3175  320 
40.6761  098 
44.3369  597 
48.3272  861 

49.7851  811 
54.7636  992 
60.2400  692 
66.2640  761 
72.8904  837 

46 
47 
48 
49 
50 

7.5744  1961 
7.9152  6849 
8.2714  5557 
8.6436  7107 
9.0326  3627 

9.4342  582 
9.9059  711 
10.4012  697 
10.9213  331 
11.4673998 

14.5904  875 
15  4659  167 
16.3938  717 
17.3775  040 
18.4201  543 

22.4726  234 
24.0457  070 
25.7289  065 
27.5299  300 
29.4570  251 

34.4740  853 
37.2320  122 
40.2105  731 
43.4274  190 
46.9016  125 

52.6767  419 
57.4176486 
62.5852  370 
68.2179  083 
74.3575  201 

80.1795  321 
88.1974  853 
97.0172  338 
106.7189  572 
117.3908  529 

INTEREST  249 

11.  What  is  the  amount  of  $216.50  at  7%  compounded  an- 
nually for  9  years? 

12.  What  is  the  compound  interest  of  $785.40  at  8%   com- 
pounded quarterly  for  11  years?    -ft fO^t I.  * 

IS.  What  is  the  compound  interest  of  $2367.25  at  10%  com- 
pounded semi-annually  for  17  years  6  months? 

14.  What  is  the  compound  interest  of  $6532.80  at  6%  com- 
pounded quarterly  for  6  years? 

Find  the  principal  that  will  yield  at  compound  interest. 

15.  $578.81J  in  three  years  at  5%,  compounded  annually. 
NOTE. — Divide  the  amount  by  amount  of  $1. 

16.  $7133.03  in  4  yrs.  3  mo.  8  days  at  1%,  compounded  an- 
nually.        *    $  5~3^£       ffl^*^.  ?0£<i&rf~/ 

17.  $1340.10  in  3  years  at  10%,  compounded  semi-annually. 

18.  $780.32  in  2  years  at  7%,  compounded  semi-annually. 

19.  $501.99  in  1  yr.  5  mo.  18  days  at  6%,  compounded  quar- 
terly. 

'20.  $987.23  in  1  yr.  10  mo.  20  days  at  8%,  compounded  quar- 
terly. 

21.  $1495.77  in  3  yrs.  7  mo.  18    days    at    5%,    compounded 
semi-annually. 

22.  What  is  the  difference  between  the  simple  interest  and 
the  compound  interest  at  8%,  on  a  note  of  $450  for  4  years,  no 
grace ;  interest  compounded  annually  ? 

23.  What  is  the  difference  between  the  annual  interest  and 
the  compound  interest  at  10%,  on  a  note  of  $660  for  2  yrs.  1  mo. 
10  days,  no  grace;  interest  payable  semi-annually,  but  not  paid 
until  maturity  ? 

24'  Find  the  difference  between  the  annual  interest  and  the 
compound  interest  at  9%,  on  a  debt  of  $750  for  1  yr.  4  mo.  15 
days ;  interest  payable  quarterly,  but  not  paid  until  maturity. 

25.  What  is  the  difference  between  the  annual  interest  and 
the  compound  interest  at  8J%  on  a  note  of  $625  for  3  yrs.  4  mo. 
18  da. ;  interest  payable  semi-annually,  but  not  paid  until  ma- 
turity ? 

26.  Find  the  difference  between  the  simple  and  compound  in- 
terest on  $925.30  at  7%,  for  15  yrs.  6  mo.  10  da.,  compounded 
semi-annually. 


COMMERCIAL  PAPER 

353.  Commercial  Paper  includes  all  written  or  printed  docu- 
ments used  as  representatives  of  money  value,  that  can  be  trans- 
ferred by  indorsement,  and  consists  of  notes,  drafts  and  checks. 

354.  A  Promissory  Note  is  a  written  promise,  signed  by  the 
person  promising,  to  pay  a  certain  sum  of  money  on  demand  or 
at  a  specified  time  for  value  received. 

355.  A  Draft  is  a  written  order  signed  by  one  party,  direct- 
ed to  another,  ordering  him  to  pay  to  a  third  party,  or  to  his  or- 
der, a  certain  sum  of  money,  either  at  sight  or  at  a  specified  time. 
Drafts  drawn  on  parties  in  other  states  or  countries  are  called 
Bills  of  Exchange. 

356.  A  Check  is  a  written  order  signed  by  a  party  having 
money  in  a  bank,  directing  the  bank  to  pay  a  certain  sum  to  a 
certain  party,  or  to  his  order,  or  bearer. 

357.  An  Indorsement  is  a  writing  on  the  back  of  commer- 
cial paper,  that 

1.  Transfers  the  ownership;  or 

2.  Secures  the  payment ;  or 

3.  Acknowledges  part  payment. 

358.  The  Parties  to  a  commercial  paper  are: 

1.  The  Maker,  who  signs  a  note. 

2.  The  Drawer,  who  signs  a  draft  or  check. 
8.  The  Payee,  who  is  to  receive  the  money. 

4.  The  Drawee,  to  whom  the  order  is  addressed. 

5.  The  Indorser,  whose  name  appears  on  the  back  of  the 
paper. 

The  original  parties  to  commercial  paper  are  those  necessary  to  create 
the  paper,  or  bring  it  into  existence. 

The  original  parties  to  a  note  are  the  maker  and  payee.  The  original 
parties  to  a  draft  or  check  are  the  drawer,  drawee  and  payee. 

The  subsequent  parties  to  commercial  paper  are  the  indorsers  and 
indorsees, 

250 


COMMERCIAL    PAPER  251 

The  holder  of  commercial  paper  is  the  owner. 

The  payer  is  the  party  who  is  to  pay  the  money  to  the  payee,  viz. :  the 
maker  of  a  note  or  the  drawee  of  a  draft  or  check. 

The  face  of  commercial  paper  is  the  sum  made  payable  by  the  paper. 

The  buyer  or  remitter  of  a  draft  or  bill  of  exchange  is  the  party  who 
sends  or  remits  it  as  the  equivalent  of  money. 

359.  A  Negotiable  Note  is  one  that  can  be  transfer-red  under 
proper  conditions  and  thus  give  the  new  holder  the  right  to  en- 
force it  against  the  maker,  irrespective  of  advance  claims,  set-offs 
or  defences. 

A  Non-Negotiable  Note  is  one  that  lacks  some  essential  feature  of  a 
negotiable  note,  and  can  only  be  transferred  so  as  to  give  the  new  holder 
such  rights  as  the  former  holder  had. 

In  order  to  be  negotiable,  commercial  paper  must  be  made  payable 
to  order  or  to  bearer.  Negotiable  paper  becomes  non-negotiable  after  it 
is  due. 

Some  states  as  Arkansas  and  Pennsylvania,  and  New  Jersey  require 
that  paper  in  order  to  be  negotiable  must  contain  some  such  expression  as 
"without  discount,"  "without  defalcation,"  or  "without  set-off."  In  these 
states  the  omission  of  these  expressions  would  not  affect  the  transferability 
but  would  affect  the  negotiability  of  the  paper. 

360.  Days  of  Grace  are  three  days  allowed  after  the  expira- 
tion of  the  time  specified,  before  the  paper  is  legally  due. 

Days  of  grace  have  been  abolished  in  a  majority  of  the  states. 

361.  The  Maturity  of  Commercial  Paper  is  the  day  on  which 
it  is  legally  due. 

362.  In  computing  time,  on  commercial  paper,  the  day  of 
date  is  omitted  and  the  day  of  maturity  is  included. 

1.  If  the  time  is  given  in  months,  calendar  months  are  meant. 
Thus — Two  months  after  January  5  ends  with  March  5. 

2.  If  there  are  not  as  many  days  in  the  month  in  which  the  time 
ends  as  were  given  in  the  first  month,  the  time  never  includes  more  than 
the  last  day  of  the  latter  month. 

•    Thus— 1  month  after  January  29,  30  or  31  ends  with  February  28  or  29. 

3.  If  the  time  is  given  in  days,  the  exact  time  must  be  computed. 
Thus — 60  days  after  December  15  ends  with  February  13. 

4.  The  banks  of  the  District  of  Columbia,  Delaware,  Maryland,  Mis- 
souri, Pennsylvania,  charge  interest  for  the  day  on  which  a  note  is  dis- 
counted and  for  the  day  on  which  it  matures — making  the  interest  period 
practically  one  day  longer  than  in  other  states. 


252  NEW   BUSINESS   ARITHMETIC 

When  the  last  day  of  grace  falls  upon  Sunday  or  a  legal  holiday,  in 
most  states,  the  paper  matures  the  previous  day,  but  if  this  also  should 
be  Sunday  or  a  legal  holiday  it  is  then  payable  one  day  earlier  still.  Where 
grace  is  not  allowed,  the  date  of  maturity  is  a  day  later  when  the  paper 
matures  on  a  Sunday  or  legal  holiday. 

363.  The    Indorsement    of    commercial    paper,    to    transfer 
ownership,  may  be  either  in  blank  or.  in  full. 

1.  An  indorsement  in  blank  is  simply  the  signature  of  the  indorser. 

2.  An  indorsement  in  full  is  an  order  over  the  signature  of  the  in- 
dorser, to  pay  to  some  other  party,  or  to  the  order  of  that  party. 

3.  An  indorsement  in  blank  makes  the  paper  payable  to  the  bearer, 

4.  The  indorser  of  a  commercial  paper  guarantees  its  payment,  and  is 
liable  for  its  payment  to  any  subsequent  holder,  unless  the  words  "with- 
out recourse,"  or  words  of  similar  import,  precede  his  signature. 

5.  Commercial  paper  made  payable  to  bearer  need  not  be  indorsed 
to  transfer  ownership ;  but,  if 

Made  payable  to  order,  it  must  be  indorsed  to  transfer  ownership. 

364.  A  Protest  is  a  formal  statement  made  by  a  Notary  Pub- 
lic, over  his  official  seal  that  a  note,  draft  or  check  has  been  prop- 
erly presented  for  payment  or  acceptance,  and  the  same  has  been 
refused. 

Commercial  paper  must  be  legally  protested  to  hold  the  in- 
dorsers  liable  for  its  payment. 

In  order  to  make  a  protest  of  commercial  paper  legal,  the  pa- 
per must  be  presented  for  payment  on  the  day  of  its  maturity, 
during  business  hours,  at  the  place  where  it  is  payable ;  and,  if  no 
place  of  payment  is  specified  in  the  paper,  at  the  residence  or 
place  of  business  of  the  maker,  during  reasonable  hours. 

365.  The  Acceptance  of  a  draft  or  check  is  the  writing,  by 
the  drawee,  across  the  face  of  the  paper,  the  word  "Accepted" 
and  the  date,  followed  by  his  signature. 

If  the  drawee  refuses  to  accept  or  to  pay  a  check  or  draft,  the  holder 
must  have  the  paper  protested,  to  hold  the  drawer  and  indorsers  liable  for 
its  payment. 

A  sight  draft  is  one  made  payable  at  sight,  or  on  demand. 

A  time  draft  is  one  made  payable  at  a  specified  time  after  sight  or  after 
date. 

When  no  time  of  payment  is  mentioned  in  commercial  paper,  it  is  pay- 
able at  sight,  or  on  demand. 

To  honor  a  draft  or  check  is  to  accept  it  or  pay  it  on  presentation. 


COMMERCIAL    PAPER  253 

366.  Promissory  notes  are  named 

1.  From  time  of  payment — as  demand  notes  and  time  notes. 

2.  From  the  maker  or  makers — as  individual  notes,  joint  notes 
and  joint  and  several  notes. 

3.  From  the  words  "with  interest"  or  from  their  omission — 
as  interest-bearing  notes  and  non-interest-bearing  notes. 

All  notes  bear  interest  after  they  become  due  if  not  then  paid,  even 
though  no  mention  of  interest  is  made  in  them. 

FORMS  OF  NOTES  AND  DRAFTS 

367.    1.      PROMISSORY    NOTE SIMPLEST    FORM 


Chicago,  III,  Dec.  18, 1903. 
Seven  months  after  date  we  promise  to  pay  Samuel  B. 

Willey or  order,  Seven  Hundred 

and  n°Jioo Dollars. 

Chas.  W .  Connors  &  Co. 


What  will  be  the  amount  due  on  the  above  note  January  1, 
1905,  finding  time  by  compound  subtraction? 

2.  NOTE INTEREST-BEARING 


$865.38.  Detroit,  Mich.,  June  20,  1905. 

Sixty  days  after  date  I  promise  to  pay  to  Henry  Graham, 
or  order,  Eight  Hundred  Sixty-Five  and  T3inr  Dollars  with 
interest  at  7% .  Value  received. 

David  G.  Lamont. 


In  finding  the  maturity  of  this  note  count  60  days  after  June  20. 

What  is  the  maturity  of  the  above  note?     VVhat  amount  will 
be  due  at  maturity  ? 


254  NEW   BUSINESS   ARITHMETIC 

3.  NOTE — NON-INTEREST-BEARING 


$1250.  Philadelphia,  Pa.,  Oct.  31,  1905. 

Four  months  after  date  I  promise  to  pay  Milton  W . 
Towns  end,  or  order,  One  Thousand  Two  Hundred  Fifty 
Dollars.  Value  received,  without  defalcation, 

Amos  dimming. 


In  finding  the  maturity  of  this  note  consult  Art.  362.  No  interest 
will  be  due  on  this  note  at  maturity,  but  if  not  paid  then  it  will  draw  in- 
terest at  the  legal  rate  in  the  state  where  it  is  given. 

What  is  the  maturity  of  the  above  note  ?  If  it  is  not  paid  until 
July  10,  1906,  what  amount  will  then  be  due,  including  $1.75 
protest  fees? 

4.  JOINT  AND  SEVERAL  NOTE 


$825.30.  Omaha,  Neb.,  May  15,  1903. 

On,  or  before  March  first,  1905,  we  jointly  or  severally 
promise  to  pay  to  Rober*  Brown  &  Co.,  or  order,  Eight  Hun- 
dred Twenty-Five  and  T%  Dollars,  value  received,  with 
interest  after  sir  months. 

Walter  S.  Thompson, 
Isaac  O.  Sibley. 


The  above  note  is  payable  "on  or  before,"  which  gives  the  payers  the 
option  of  paying  the  note  at  their  convenience  at  any  time  before  due.  In 
a  joint  note  both  makers  must  be  sued  together.  A  joint  note  reads  "we 
promise,"  etc.,  while  a  joint  and  several  note  reads  "we  jointly  or  sever- 
ally." In  a  joint  and  several  note  each  maker  is  separately  liable  for  the 
full  amount  of  the  note,  and  can  be  sued  separately.  Interest  on  the  above 
note  does  not  begin  until  six  months  after  the  date. 

Suppose  the  above  note  is  settled  November  15,  1904.  What 
amount  must  be  paid? 


COMMERCIAL    PAPER  255 

5.  SIGHT    DRAFT 


$200.00.  Cincinnati,  Ohio,  Dec.  16,  1905. 

At  sight  pay  to  the  order  of  Andrew  Wilson,  Two  Hundred 
Dollars,  value  received,  and  charge  to  account  of 

To  A.  J.  Cooper  &  Co.,      )    T  TT7    ^  or- 

Detroit,  Mich.  \  ]ames  W'  Cameron  &  Co~ 


In  the  state  of  Michigan  sight  drafts  are  allowed  days  of  grace,  hence 
this  draft  should  be  accepted  by  A.  J.  Cooper  &  Co.,  by  writing  "Ac- 
cepted" with  date  and  signature  across  the  face  of  the  draft.  The  draft 
will  then  be  due  three  days  after  such  acceptance. 

6.  TIME  DRAFT 


$1739.00.  Columbus,  O.,  May  10,  1905. 

At  thirty  days  sight  pay  to  the  order  of  Marshall  Field  & 
Co.,  One  Thousand  Seven  Hundred  Thirty-Nine  Dollars, 
value  received  and  charge  to  account  of 

To  H.  B.  Claflin  &  Co.      )      Wm_  L   churMl  &  Co_ 
New  York.  \ 


Suppose  the  above  draft  is  accepted  May  16,  1905,  when  will 
it  mature  ? 

PARTIAL   PAYMENTS 

368.  A  Partial  Payment  is  a  payment  of  a  part  of  a  note  or 
obligation. 

369.  An  Indorsement  in  Partial  Payments  is  the  acknowledg- 
ment of  the  payment,  written  on  the  back  of  the  paper  stating 
the  amount  and  the  date  of  payment. 

1.  PROMISSORY  NOTE 


$600.  Chicago,  III.,  May  1,  1903. 

On  demand  I  promise  to  pay  John  Downing,  or  order, 
Six  Hundred  Dollars,  value  received,  with  interest  at  6% 
from  date. 

William  Smith. 


256  NEW   BUSINESS   ARITHMETIC 

BACK  OF  NOTE  SHOWING  INDORSEMENTS 


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The  above  note  was  settled  May  1,  1905.  What  was  the  amount 
•due  at  settlement? 

SOLUTION 


Date 

Time 

Interest 

Amount 

Payment 

Principal 

May  1,  1903 

6# 

$600 

Aug.  12,  1903 

3  mo.  11  da. 

$10.10 

$610.10 

$75 

$535.10 

July  24,  1904 

11  mo.  12  da. 

$30.50 

$565.60 

$200 

$365.60 

May  1,  1905 

9  mo.  7  da. 

$16.88 

$382.48 

Ans. 

The  foregoing  problem  has  been  solved  according  to  the  fol- 
lowing rule  adopted  by  the  Supreme  Court  of  the  United  States 
and  hence  called  the 

United  States  Rule 

a.  Find  the  amount  of  the  given  principal  from  the  date  of  the 
note  until  the  first  payment;  if  the  payment  is  greater  than  the 
interest,  subtract  the  payment  from  the  amount,  and  treat  the  re- 
mainder as  a  new  principal.    Thus  continue  until  the  date  of  set- 
tlement. 

b.  If  the  interest  be  greater  than  any  payment,  find  the  interest 
en  the  principal  to  a  time  when  the  sum  of  the  payments  exceeds 
the  interest,  subtract  the  sum  of  the  payments  from  the  amount 
of  the  principal,  and  treat  the  remainder  as  a  new  principal. 

2.  On  a  note  dated  January  1,  1903,  for  $300  bearing  6%  in- 


COMMERCIAL    PAPER  257 

terest,  the  following  indorsement  was  made:     January  1,  1904, 
$70.    What  was  due  January  1,  1905? 

3.  On  a  note  of  $980  for  4  years  at  8%,  dated  July  5,  1902, 
the  following  payments  are  made :  March  7,  1903,  $170 ;  Jan- 
uary 5,  1904,  $25;  April  20,  1905,  $320.  What  is  due  at  ma- 
turity, July  5,  1906? 

4-  The  following  payments  were  made  on  a  mortgage  of 
$1250  bearing  7%,  dated  October  20,  1903;  $125  on  January  29, 
1904 ;  $145  on  April  8,  1904 ;  $300  on  September  20,  1904 ;  $90 
June  2,  1905.  What  was  due  November  6,  1905? 

5.  On  a  note  dated  July  15,  1903,  for  $1100  are  the  following 
indorsements:  February  24,  1904,  $200;  March  30,  1905,  $225; 
April  12,  1906,  $250 ;  June  6,  1907,  $340.  What  is  due  .Septem- 
ber 1,  1907,  interest  at  9%  ? 

6.  A  note  of  $900,  bearing  10%  interest,  dated  August  1, 
1902,  was  indorsed  as  follows:     November  13,  1902,  $115;  Feb- 
ruary 25,  1903,  $125;  June  7,  1903,  $20;  October  28,  1903,  $200; 
January  1,  1904,  $340.    What  was  due  April  25,  1904? 

7.  April  1,  1902,  a  note  was  given  for  $7500  at  5%  interest. 
Payments  were  made  on  September  15,  1902,  of  $1000 ;  on  July 
27,  1903,  of  $870;  on  March  6,  1904,  of  $2400;  on  August  27, 
1904,  of  $1130.    What  was  due  February  18,  1905? 

8.  A  note  of  $1575,  bearing  6%  interest,  dated  January  1, 
1902,  for  3  yrs.  8  mo.,  was  indorsed  July  20,  1902,  $250;  Feb- 
ruary 6,  1903,  $200;  January  10,  1904,  $450.     What  was  due  at 
maturity  ? 

9.  A  note  of  $1400,  bearing  10%  interest,  dated  May  1, 1905, 
for  2  yrs.  3  mo.,  was  indorsed  October  30,  1905,  $300;  June  22. 
1906,  $160;  December  5,  1906,  $200.     How  much  was  due    at 
maturity  ? 

10.  A  note  for  $10000  dated  January  1,  1900,  bearing  6%  in- 
terest was  indorsed  as  follows :  May  1,  1900,  $18 ;  September  4, 
1900,  $20;  December  16,  1900,  $15;  April  10,  1901,  $21;  July 
13,  1901,  $125;  December  23,  1901,  $324.  What  was  due  at  the 
time  of  settlement,  November  1,  1903? 

370.  The  following  rule  is  used  by  banks  and  generally  by 

17 


258 


NEW   BUSINESS   ARITHMETIC 


merchants  in  finding  the  sum  due  on  a  note  when  partial  pay- 
ments have  been  made.  The  banker's  interest  is  reckoned  in  this 
rule. 

Merchants'  Rule 

a.  Find  the  amount  of  the  note  from  the  time  it  zvas  given 
until  the  time  of  settlement. 

b.  Find  the  amount  of  each  payment  from   the   time   it   zuas 
made  until  the  time  of  settlement. 

c.  From  the  amount  of  the  principal,,  subtract  the  amount  of 
the  payments. 


1.  On  a  note,  dated  Jan.  1,  190 4-,  for  one  year,  for  $560, 
interest  6%,  the  following  payments  were  made:  June  1,  1904, 
$65,  and  Nov.  15,  1904,  $100.  Find  the  sum  due  at  maturity. 

In  computing  the  interest  under  the  Merchants'  Rule,  find 
the  exact  time  in  days,  and  consider  a  year  360  days. 


SOLUTION 


Date 

Time 

Interest 

Payment 

Amount 

Balance 

Jan.  1,  '04-Jan.  1,  '05 
June  1,  '04—  Jan.  1,  '05 
Nov.  15/04—  Jan.  1/05 

360  da. 
214  da. 
47  da. 

6£ 
$33.60 

$2.32 
$  .78 

$65. 
$100. 

$560. 
$593.60 
$67.32 
$100.78 
Ans. 

$593.60 
$168.10 

$425.50 

2.  Find  the  sum  due  on  December  10,  1905,  on  a  note  of 
$900,  at  6%  interest,  dated  April  1,  1905,  and  indorsed  July  6, 
1905,  for  $240;  September  12,  1905,  for  $420. 

3.  What  sum  is  due  November  17,  1905,  on  a  note  of  $2850, 
at  8%  interest,  dated  March  12,  1905,  and  indorsed  as  follows: 
May  30,  1905,  $850;  August  24,  1905,  $700;  October  6,  1905, 
$470? 


COMMERCIAL    PAPER  259 

4.  On  a  note,  dated  March  1,  1905,  for  9  months,  of  $765,  at 
interest,  the  following  payments  were  made :    April  26,  $140  ; 

June  20,  $280 ;  November  6,  $295.     Find  the  sum    due    at    ma- 
turity. 

5.  A  note  for  $1800  at  1%  interest  was  given  September  2, 
1905,  payments  were  made  December  28,  1905,  of  $480;  March 
1,  1906,  of  $325 ;  May  23,  1906,  of  $670.    What  was  due  at  ma- 
turity, the  time  of  the  note  being  10  mo.  12  days? 

6.  A  note  of  $3500  with  interest  at  10%,  dated  October  30, 
1905,  was  indorsed  as  follows:    January  1,  1906,  $1100;  March 
20,  1906,  $390 ;  June  2,  1906,  $845.     What  was  due  September 
16,  1906? 

7.  A  note  of  $1780,  bearing  S%  interest,  dated  August  27, 
1905,  for  8  months,  was  indorsed  on  November  10,  1905,  $275; 
on  February  3,  1906,  $600.    What  was  due  at  maturity? 

8.  A  note  of  $1065,  bearing  6%  interest,  dated  January  1, 
1905,  for  7  mo.  15  days,  was  indorsed  on  March  4,  $200 ;  on  May 
12,  $180;  on  May  30, -$300.     What  was  the  amount  due  at  ma- 
turity? 

9.  What  is  the  difference  between  the  sum  due  by  United 
States  Rule  and  Merchants'  Rule,  on  a  note  of  $720,  bearing  5% 
interest,   dated   February   2,   for   8   mo.    10   days,   and   indorsed 
April  4,  for  $160;  June  11,  $210;  August  1,  $80? 

10.  Which  is  greater  and  how  much,  the  sum  due  by  United 
States  Rule  or  the  sum  due  by  Merchants'  Rule  on  a  note  of  $810 
at  10%  interest,  dated  November  19,  1905,  for  10  months,  and 
indorsed  January  1,  1906,  for  $230;  March  16,  1906,  for 
April  4,  1906,  for  $360? 

(11) 


$1248.  Boston,  Mass.,  December  11,  1905. 

Seven  months  after  date,  I  promise  to  pay  S.  M.  Mack,  or 
bearer,  Twelve  Hundred  Forty-eight  Dollars.  Value  received, 
interest  at  7%  from  date.  Payable  at  Second  National  Bank. 

R.  S.  Wilco.v. 


The  following  indorsements  were  made :    January  25,  $100 ;  March  16, 
$350;  April  16,  $50;  May  10,  $225.    What  was  due  at  maturity? 


260  NEW   BUSINESS   ARITHMETIC 

371.  Annual  Interest  with  Partial  Payments. 

In  case  interest  is  payable  annually  and  partial  payments  have 
been  made  at  irregular  intervals,  the  following  rule  is  the  method 
of  solution. 

a.  Find  the  interest  on  the  principal  for  the  first  interest  period, 
and  find  also  the  amounts  of  the  payments  made  during  this 
period,  from  the  times  they  were  severally  made  until  the  end  of 
the  period. 

b.  If  the  payments  amount  to  more  than  the  interest  due,  take 
their  amount  from  the  amount  of  the  principal,  and  make  the  re- 
mainder a  new  principal. 

c.  But  if  the  amount  of  the  payments  does  not  equal  the  inter- 
est due,  the  principal  remains  unchanged;  and  the  amount  of  the 
payments  is  taken  from  the  interest,  the  remainder  being  treated 
as  deferred  interest. 

d.  This  deferred  interest  draws  interest  until  it  is  paid,  or  until 
the  note  matures;  and  all  payments  apply;  firstly,  to  interest  on 
deferred  interest;  secondly,  to  deferred  interest;  and  lastly,  to  in- 
terest just  due,  and  principal. 

1.  What  amount  will  be  due  on  a  note  dated  January  1,  1902, 
due  in  5  years  for  $6000,  drawing  interest  at  6%  payable  an- 
nually, the  following  payments  having  been  made  thereon :     May 
1,  1904,  $500;  September  1,  1906,  $800. 

2.  A  note  for  $1200,  at  6%  interest,  payable  annually,  is  dated 
June  16,  1900,  and  is  to  run  five  years.     No  interest  having  been 
paid  except  for  the  first  year,  and  the  following  payments  having 
been  made,  viz.:     September  15,   1902,  $250;  March  10,   1904, 
$400.    What  amount  will  be  due  at  maturity  ? 


TRUE  DISCOUNT 

372.  Discount  is  a  deduction  made  for  the  payment  of  money 
before  it  is  due. 

373.  The  Present  Worth  of  a  debt  due  at  a  future  time  is  its 
value  now.    The  present  worth  of  a  debt  is  such  a  sum  as,  if  put 
at  interest,  will  amount  to  the  debt    at    the    expiration    of    the 
time. 

374.  True  Discount  is   the   difference   between   the   present 
worth  and  the  debt,  and  is  called  true  discount  because  the  method 
of  computing  it  is  in  strict  accordance  with  equity. 

True  discount  is  little  used  owing  to  the  difficulty  in  comput- 
ing it,  and  bank  discount  has  almost  become  universal. 

375.  The  Face  of  the  Debt  is  the  sum  which  will  be  due  at 
the  expiration  of  the  time. 

The  Present  Worth  is  a  Principal  which  at  the  rate  of  interest 
for  the  time  will  amount  to  the  debt. 

The  terms  Present  Worth,  Face  of  Debt  and  True  Discount 
correspond  to  Principal,  Amount  and  Interest. 

1.  What  is  the  present  worth  and  true  discount  of  a  debt  of 
$354  due  in  3  yrs.,  money  being  worth  6%? 
SOLUTION 

1.  3  X  $-06  =  $.18. 

2.  Int.  on  $1  =  $.18. 

3.  $1  +  $.18  =  =?  $1.18  amount  of  $1. 

4.  $354  -=-  $1.18  =  $300  present  worth. 

5.  $354  —  $300  =  $54  true  discount. 

From  this  solution  and  explanation  we  have  the  following : 

To  Find  the  True  Discount 

a.  Divide  the  face  of  the  debt  by  the  amount  of  $1  for  the 
given  time  and  rate,  and  the  result  will  be  the  present  worth. 

b.  Subtract  the  present  worth  from  the  face  of  the  debt  and 
the  difference  will  be  the  true  discount. 

NOTE. — In  the  following  problems  the  rate  per  cent,  is  6,  unless  some 
other   rate   is   given. 

2G1 


262  NEW   BUSINESS   ARITHMETIC 

2.  I  owe  $191.08,  due  in  1  yr.  6  mo.  18  days.    I  am  allowed 
true  discount  at  8%.    Find  the  sum  that  will  pay  the  debt  now.$V 

3.  What  sum  will  pay  a  debt  of  $1098.39,  due  in  2  yrs.  9  mo. 
21  days,  money  being  worth  6%  ? 

4.  My  note  of  $1035.99,  due  in  3  yrs.  1  mo.  6  days,  was  pur- 
chased by  B  at  9%  true  discount.    What  did  he  pay  for  the  note? 

5.  L.  B.  Jones  owes  $1657.50,  due  in  5  yrs.  11  mo.  3  days. 
He  borrowed  the  money  to  pay  same,  being  allowed  4%  true  dis- 
count.   How  much  did  he  borrow? 

6.  If  Parker  pays  a  debt  of  $151.27,  due  in  1  yr.  1  mo.  24 
days,  with  corn  at  35  cents  per  bushel,  how  many  bushels  will 
be  required,  money  being  worth  7%? 

7.  Brown  gave  his  note  for  $470,  and  cash  for  remainder,  of  a 
debt  of  $1073.50,  due  in  2  yrs.  2  mo.     How  much  cash  did  he 
pay,  if  he  was  allowed  6%  true  discount  on  the  debt? 

8.  I  gave  Smith  a  horse  in  payment  of  a  debt  of  $193.60,  due 
in  8  mo.  12  days.    I  was  allowed  10%  true  discount  on  the  debt, 
and  thus  gained  20%  on  the  cost  of  the  horse.     What  did  the 
horse  cost  me  ? 

9.  A  merchant  purchased  a  bill  of  goods    for    $260    on    6 
months'  time,  or  $245  for  cash.     If  money  is  worth  8%,  will  he 
gain  or  lose  and  how  much  if  he  pays  cash  ? 

10.  A  jobber  paid  $274  cash  for  a  lot  of  merchandise,  rather 
than  give  his  note  for  $297.30  for  1  yr.  6    mo.     If   money   was 
worth  7%,  what  did  he  lose  by  paying  cash? 

11.  A  merchant  bought  a  bill  of  goods  for  $760  on  1  year's 
time,  or  with  a  trade  discount  of  2  and  5%  for  cash.    He  accepted 
the  cash  offer.    Did  he  gain  or  lose,  money  being  worth  6f  %  ? 

12.  I  bought  $721  worth  of  wheat  on  4  months'  time,  and  sold 
it  on  same  day  at  12%  advance.    I  paid  the  present  worth  of  the 
debt  from  the  proceeds,  being  allowed  9%  true  discount.     How 
much  did  I  gain  by  the  transaction? 

13.  A  wholesale  merchant  sold  a  bill  of  $1020  at  a  trade  dis- 
count of  20  and  124%,  and  allowed  a  credit  of  90  days.    He  ac- 
cepted cash  payment  allowing  true  discount  at  8%.     What  was 
the  cash  payment? 


TRUE    DISCOUNT  263 

14-  A  retail  merchant  bought  a  bill  of  goods  amounting  to 
$360 .at  a  trade  discount  of  10  and  5%.  He  sold  the  goods  at 
20%  profit  on  the  invoice  price  and  allowed  a  credit  of  6  months. 
What  was  his  net  gain,  money  being  worth  W%  ? 

15.  I  sold  goods  for  $1134,  and  allowed  7  mo.  15  days  credit. 
The  purchaser  paid  me  cash  at  true  discount  of  S%.  I  invested 
the  proceeds  in  wheat  at  $1.20  per  bushel.  How  many  bushels 
did  I  buy? 


BANK  DISCOUNT 

376.  Bank  Discount  is  the  simple  interest  paid  in  advance  on 
a  note  or  draft  for  the  time  the  paper  has  to  run. 

Bank  Discount  may  be  computed  by  either  of  the  methods  of  reckon- 
ing interest,  but  in  the  case  of  notes  discounted  in  banks,  and  call  loans 
on  Wall  street  banker's  interest  is  used. 

377.  The  Proceeds  of  a  note  or  draft  is  the  sum  received 
from  the  bank  for  it  or  the  face  of  the  paper  less  the  bank  dis- 
count. 

In  case  the  paper  is  drawing  interest,  the  amount  due  at  maturity  is 
the  face  of  the  paper  and  on  this  the  discount  should  be  computed. 

378.  The  Term  of  Discount  is  the  time  from  the  date  of  dis- 
count to  the  maturity  of  the  paper. 

In  finding  the  term  of  discount  the  usual  custom  is  to  exclude  the  day 
on  which  the  paper  is  discounted,  but  include  the  day  of  maturity.  Thus 
on  a  note  discounted  June  10,  due  June  25,  the  term  of  discount  would 
be  15  days.  This  custom  is  not  universal  however,  and  banks  in  Baltimore, 
Philadelphia  and  few  other  cities,  charge  for  the  day  of  discount,  also, 
making  in  the  above  example  16  days  as  the  term  of  discount. 

In  computations  in  bank  discount,  five  quantities  are  consid- 
ered, viz. :  Face  of  Debt,  Rate  of  Discount,  Term  of  Discount, 
Bank  Discount  and  Net  Proceeds. 

In  the  following-  problems,  do  not  use  grace  and  count  exact 
days  for  term  of  discount. 

379.  To  find  the  bank  discount  and  proceeds  of  a  note  or 
debt. 

1.  Find  the  bank  discount  and  the  proceeds  of  a  note  of  $240 
at  6%  discount,  dated  January  10,  1903,  for  4  mo.  27  days. 

SOLUTION 

Jan.  10  +  4  mo.  27  da.  =  June  6. 

From  Jan.  10  to  June  6          =  147  da. 
Face  of  note  =  $240. 

Int.  on  $1  for  147  da.  at  6%  =  .0245. 
Bank  discount  =  $5.88. 

Proceeds  =  $240  —  $5.88     =  $234.12. 

264 


BANK    DISCOUNT  265 

From  this  solution  and  explanation  we  have  the  following: 
To  Find  the  Bank  Discount 

a.  Find  the  term  of  discount  in  exact  days. 

b.  Find  the  interest  on  the  face  of  the  note  for  the  term  of 
discount  and  this  ivill  be  the  bank  discount. 

c.  Subtract  the  discount  from  the  face  of  the  note  to  find  the 
net  Proceeds. 

NOTE. — If  a  note  is  on  interest,  find  its  amount  at  maturity,  and  taking 
this  as  the  face  of  the  note,  cast  the  interest  on  it  as  above. 

Find  the  bank  discount  of  the  following  notes  (no  interest): 

2.  $325,  dated  March  4  for  2  mo.  26  days,  discounted  March 
18  at  5%. 

3.  $870,  dated  May  1  for  27  days,  discounted  May  11  at  9%. 

4.  $465,  dated  April  16,  for  1  mo.  12  days,  discounted  April 
27  at  7%. 

5.  $1282.50,  dated  February   19,    1905,   for  3  mo.   4  days, 
discounted  March  23  at  8%. 

6.  $1848,    dated  January  27,  1905,  for  4  mo.  2  days,   dis- 
counted at  10%  on  the  day  of  making. 

Find  the  proceeds  of  the  following  non-interest-bearing  notes : 

7.  $920,  dated  January  10,  1905,  due  in  30  days,  discounted 
January  10  at  10%. 

8.  $465,  dated  March  4,  1905,  due  in  60  days,   discounted 
March  15  at  9%. 

9.  $2725,  dated  November   12,  1905,   due  in  90  days,   dis- 
counted November  17  at  5%. 

10.  $194.80,  dated  September  4,  1905,  due  in  45  days,  dis- 
counted September  4  at  6%. 

Find  the  date  of  maturity,  term  of  discount,  bank  discount 
and  proceeds  of  the  following  notes. 

(11) 

$280.  CHICAGO,  ILL.,  March  12,  1905. 

Four  months  after  date,  I  promise  to  pay  to  R.  T.  OWENS,  or 
order,  Two  Hundred  Eighty  Dollars.  Value  received. 

F.  S.  Cox. 

Discounted  May  20,  1905,  at  7%. 


266  NEW   BUSINESS   ARITHMETIC 

(12) 
$970.  LANSING,  MICH.,  August  25,  1905. 

Six  months  after  date,  I  promise  to  pay  to  the  order  of  G.  H. 
GRAHAM,  Nine  Hundred  Seventy  Dollars.  Value  received.  In- 
terest at  5%  from  date. 

C.  H.  SMITH. 
Discounted  November  6,  1905,  at  7%. 

NOTE. — Find  the  amount  due  at  maturity,  and  compute  the  discount  on 
this  amount  from  November  6,  to  maturity. 

(IS.     JOINT  NOTE) 
$1280.  LOUISVILLE,  KY.,  January  1,  1905. 

Nine  months  after  date,  we  promised  to  pay  E.  H.  DURANT,  or 
bearer,  Twelve  Hundred  Eighty  Dollars.  Value  received,  with 
interest  at  8%  from  date. 

THOMAS  SMAILS. 
J.  D.  PETERS. 
Discounted  July  15,  1905,  at  6%. 

(14-    SEVERAL  NOTE) 
$1968.40.  FREMONT,  NEB.,  June  5,  1905. 

One  year  after  date,  either  of  us  promises  to  pay  R.  D.  ALLEN 
&  Co.,  or  order,  Nineteen  Hundred  Sixty-eight  tVV  Dollars. 
Value  received,  with  interest  at  1%.  Payable  at  the  Merchants 
Bank. 

G.  H.  MAHLER. 
O.  A.  PRESTON. 
J.  B.  Ross. 
Discounted  April  1,  1906,  at  10%. 

(15.      JOINT  AND  SEVERAL  NOTE) 

$292.50.  CHICAGO,  ILL.,  July  14,  1905. 

Nine  months  and  twelve  days  after  date,  we  or  either  of  us, 
promise  to  pay  to  the  order  L.  P.  DERN,  Two  Hundred  Ninety- 
two  r5A  Dollars.  Value  received,  with  interest  at  9%. 

J.  F.  SOMERS. 
P.  R.  CORBIN. 
A.  C.  WILSON. 

Discounted  January  1,  1906,  at  8%. 

16.  Find  the  proceeds  of  a  note  of  $275,  bearing  6%  interest, 
dated  March  19,  1905,  payable  in  3  months;  discounted  April  16, 
at  S%. 


BANK    DISCOUNT  267 

17.  I  held  B's  note  of  $1760,  bearing  10%    interest,    dated 
February  6,  1905,  for  5  months,  10  days,  and  discounted  same 
May  1,  1905,  at  6%.    How  much  did  I  receive  from  the  bank? 

18.  A  merchant  who  had  a  credit  of  $368.72  at  the  bank,  had 
the  proceeds  of  the  following  note  placed  to  his  credit :    $628.80, 
bearing  8%  interest,  dated  January  17,  1905,  for  7  months,  dis- 
counted April  2,  1905,  at  S%.    What  was  his  credit  then? 

19.  Lyman  discounted  a  note  of  $1600,  bearing  W%  interest, 
dated  April  3,  1905,  for  10  months ;  discounted  August  12,  1905, 
at  1%.     How  much  was  left  after  paying  with  the  proceeds  a 
note  of  $630,  that  had  been  on  interest  2  years  at  S%  ? 

20.  For  what  sum  must  I  give  my  note  for  60  days  to  receive 
$600  proceeds,  if  the  note  is  discounted  at  8%  ? 

NOTE.— Since  the  proceeds  of  $1  at  8%  for  60  days  is  .986^  it  will  re- 
quire as  many  dollars  to  produce  $600  proceeds  as  .986^  is  contained  in 
$600  or  $608.11. 

21.  I  received  $711  from  a  bank  on  a  90  days'  note,  at  5% 
discount.    What  was  the  face  of  the  note  ? 

22.  What  must  be  the  face  of  a  note  for  105  days,  to  give 
$536.80  proceeds  when  discounted  at  10%  ? 

28.  $1186.50  was  the  proceeds  of  a  note,  dated  January  18 
for  4  months,  and  discounted  April  3,  at  9%.  What  was  the 
face? 

2Jf.  The  discount  on  a  note,  dated  February  6  for  6  months, 
and  discounted  July  7  at  10%  is  $12.50.  Find  the  face  and  the 
proceeds  of  the  note. 

NOTE. — Divide  the  discount  by  the  discount  on  $1,  to  find  the  face 
of  the  note. 

25.  Smith's  note,  dated  March  1  for  4  mo.  15  days  was  dis- 
counted May  2  at  1%.     What  was  the  face  of  the  note,  if  the 
discount  was  $5.25? 

26.  I  received  $581.55  at  the  bank  for  my  note  due  in  90 
days.     The  bank  charged  me  8%  discount.     What  was  the  face 
of  the  note  ? 

27.  For  what  sum  must  I  give  my  note  at  the  bank  for  2  mo. 
9  da.  to  receive  $1176,  if  the  bank  charges  9%  discount? 


STOCKS  AND  BONDS 

380.  Stocks  represent  the  capital  or  property  of  an  incorpor- 
ated company. 

381.  An  Incorporated  Company  is  an  association  authorized 
by  law  to  transact  business  as  a  single  individual. 

382.  A  Charter  is  a  legal  instrument  defining  the  powers  and 
duties  of  a  corporate  body. 

383.  The  Capital  Stock  is  the  funds  or  capital  of  the  cor- 
poration. 

384.  A  Share  is  one  of  the  equal  parts  of  the  stock.    A  share 
is  usually  $100,  though  it  may  be  of  any  value  agreed  upon  by  the 
members  of  the  corporation. 

385.  A  Stock  Certificate  is  a  paper  issued  by  a  corporation 
stating  the  number  of  shares  to  which  the  holder  is  entitled,  and 
the  par  value  of  each  share. 

386.  The  Par  Value  of  stock  is  the  value  named  in  the  cer- 
tificate. 

387.  The  Market  Value  of  stock  is  the  price  per  share  for 
which  it  sells. 

388.  Stock  is  At  Par  when  it  sells  for  its  face  value. 

389.  Stock  is  Above  Par  when  it  sells  for  more  than  its  face 
value,  and  Below  Par  when  it  sells  for  less  than  its  face  value. 

390.  Preferred  Stock   is  that  which  takes  preference  over 
common  stock  in  reference  to  dividends. 

Preferred  Stock  is  issued  as  a  special  inducement  to  raise  money  or  to 
protect  a  certain  class  of  shareholders  who  may  have  advanced  money  to 
relieve  a  company  from  embarrassment. 

391.  A  Dividend  is  the  sum  paid  to  stockholders  from  the 
gains  of  the  corporation. 

392.  Assessments  are  sums  levied  on  stockholders  to  meet 
the  expenses  or  losses  of  the  corporation. 

393.  A  Stock  Broker  is  a  person  who  buys  and  sells  stock 


as  an  agent  for  others. 


268 


STOCKS    AND    BONDS  269 

394.  Brokerage  is  the  sum  paid  to  brokers  for  buying  and 
selling  stock. 

395.  Quotations  of  Stock  are   statements  made  giving  the 
price  at  which  stock  is  being  bought  and  sold.     Stock  quoted  at 
105}-  is  selling  at  5%%  premium,  at  87J  is  selling  at  12%%  dis- 
count. 

Margin  is  cash  or  other  security  deposited  with  a  broker  on  account  of 
either  the  purchase  or  sale  of  securities,  and  to  protect  him  against  loss 
in  case  the  market  price  of  the  securities  bought  or  sold  varies  so  as  to  be 
against  the  interests  of  the  customer.  It  is  usually  10%  of  the  par  value 
of  the  stock. 

NOTE. — Brokers  charge  interest  on  the  sums  expended  and  purchase 
commission,  and  allow  interest  on  the  margins  deposited,  or  preferably 
they  charge  interest  on  the  debit  balance. 

A  Bear  is  an  operator  who  believes  the  market  price  of  stocks  will  fall. 

A  Bull  is  an  operator  who  believes  the  market  price  of  stocks  will  ad- 
vance. 

NOTE. — Hence  a  bull  will  buy  stocks  in  order  to  profit  by  the  higher 
price  at  which  he  expects  to  sell,  and  a  bear  will  sell  in  order  to  profit 
by  the  lower  price  at  which  he  expects  to  buy. 

Hypothecating  stocks  and  bonds  is  depositing  them  as  collateral  se- 
curity for  money  borrowed. 

NOTE. — The  securities  must  be  greater  than  the  loan  by  at  least  10% 
of  their  par  value,  and  in  every  case  by  an  amount  equal  to  20%  of  the 
amount  of  the  loan.  This  excess  is  called  the  margin  of  the  loan. 

Watering  Stock  is  increasing  the  number  of  shares  of  an  incorporated 
company  without  a  corresponding  increase  in  their  value. 

A  Corner  is  produced  when  one  or  more  operators  owning  or  con- 
trolling all  the  stock  of  a  company  are  able  to  purchase  still  more  for 
either  immediate  or  future  delivery.  When  they  demand  the  stock,  the 
sellers  are  unable  to  find  it  in  the  market. 

396.  A  Bond  is  a  written  or  printed  obligation  of  a  city, 
county,  state,  government  or  corporation,  promising  to  pay  a  cer- 
tain sum  of  money  at  a  specified  time. 

The  object  of  a  bond  is  to  secure  payment  of  borrowed  money.  When 
a  city,  state,  etc.,  borrows  money  it  gives  a  Bond  as  a  certificate  of  the  in- 
debtedness. 

397.  A  Coupon  Bond  is  one  having  interest  certificates  or 
coupons  attached.    They    are    transferable    merely    by    delivery, 
and  for  this  reason  are  preferred  for  purposes  of  investment. 


270  NEW   BUSINESS   ARITHMETIC 

398.  A  Registered  Bond  is  one  payable  to  the  holder,  and  is 
registered  in  the  books  of  the  authority  issuing    it.      It    can    be 
transferred  by  assignment  only. 

Bonds  are  named  from  the  authority  that  issued  them,  their  rate  of  in- 
terest, and  their  date  of  maturity.  U.  S.  "4's  of  1907"  are  bonds  issued 
by  the  United  States,  bearing  4%  interest  and  maturing  in  1907.  Chicago 
"3's  of  1900"  are  bonds  issued  by  the  city  of  Chicago,  bearing  3%  interest 
and  maturing  in  1900. 

399.  Government  Bonds  were  issued  to  secure  the  payment 
of  money  borrowed  to  meet  the  expenses  of  the  civil  war. 

400.  The  Interest  on  bonds  is  usually  paid  quarterly  or  semi- 
annually. 

401.  The  Interest  on  Government  (U.  S.)  bonds  is  payable 
in  gold,  and  is  reckoned  by  the  method  of  exact  interest. 

402.  The  Interest  on  all  bonds  except  U.  S.  bonds  is  payable 
in  currency,  and  is  reckoned  by  the  method  of  common  interest. 

403.  A  Mortgage  is  a  conveyance   of   real    estate   or    other 
property,  as  a  pledge  to  secure  the  payment  of  a  certain  debt. 

When  money  is  borrowed  to  build  a  railroad  or  for  other  purpose, 
the  payment  of  the  bonds  is  secured  by  a  mortgage  or  deed  of  trust  upon 
the  real  estate  of  the  road  made  in  favor  of  some  bank  or  trust  company 
as  trustee. 

Computations  in  Stocks  and  Bonds  are  based  upon  the  princi- 
ples of  Percentage,  and  embrace  five  quantities,  viz. :  Par  Value 
=  Base;  Rate  of  Premium  or  Discount  =  Rate;  Premium  or 
Discount  =  Percentage;  Market  Value  above  par  =  Amount; 
Market  Value  below  par  =  Difference. 

NOTE. — The  par  value  of  all  stocks  and  bonds  in  the  following  prob- 
lems is  $100  unless  otherwise  stated. 

ORAL  PROBLEMS 

1.  What  is  the  par  value  of  25  shares  of  stock?  75  shares? 
125  shares?  4  shares? 

2.  What  is  the  par  value  of  50  half    shares    of    stock?    25 
shares?    75  shares?    125  shares? 

3.  What  is  the  value  of  40  quarter    shares    of    stock?    50 
shares?  75  shares? 


UNIVERSITY 

°F 

STOCKS    AND    BONDS  271 


4.  What  puts  stock  at  a  premium?  at  a  discount? 

5.  What  is  the  premium  at  6J%  on  100  shares  of  stock?  120 
shares  ?  40  shares  ? 

6.  What  is  the  discount  at  12$%  on  240  shares  of  stock?  20 
shares  ? 

7.  What  is  the  brokerage  at  \%  on  stock,  the  par  value  being 
$7200?  $400? 

8.  What  will  20  shares  of  bank  stock  cost  at  125  and  brok- 
erage at  \%  ? 

9.  What  is  the  brokerage  on  40  shares  of  stock,  market  value 
124  J,  brokerage  at  \%  ?    What  is  the  cost  ? 

10.  I  send  my  broker  $5000  and  instruct  him  to  buy  40  shares 
of  railroad  stock  at  150,  the  value  increases  and  I  direct  him  to 
sell  at  175.  How  much  has  he  to  my  credit,  brokerage  in  each 
case  at  £%? 

WRITTEN  PROBLEMS 

1.  A  corporation  made  an  assessment  of  9%.     How  much 
will  a  stockholder  who  holds  42  shares  of  stock  pay? 

2.  I.  sold  38  shares  of  city  bank  stock  at  8%  premium.    Find 
the  amount  above  par  I  received. 

3.  A  sold  54  shares  of  stock  at  o%  discount.    For  how  much 
below  par  did  he  sell  the  stock  ? 

4.  33  shares  of  Rock  Island  stock  were  sold  at  107J.     Find 
the  amount  of  premium  received. 

5.  B  received  a  dividend  of  6f  %  on  27  shares  of  Missouri 
Pacific  stock.    What  was  the  amount  of  the  dividend? 

6.  Smith  was  assessed  13%  on  19  shares  of  mining  stock. 
Find  the  amount  of  his  assessment. 

7.  What  assessment  is  paid  by  the  holder  of  45  shares  of 
Western  Union  stock,  if  the  rate  is  4f  %  ? 

8.  Bailey  sold  78  shares  of  New  York  Central  stock  at  129J. 
Find  amount  above  par  value  he  received. 

9.  Barton  sold  46  shares,  par  value  $50,  at  a  discount  of 
9J%  ;  and  72  shares,  par  value  $25,  at  a  discount  of  !$%.  Find 
the  total  sale. 


272  NEW   BUSINESS   ARITHMETIC 

NOTE. — Multiply  the  par  value  by  the  cost  of  $1  worth  of  the  stock, 
to  find  the  market  value. 

10.  Find  the  selling  price  of  75  shares  of  stock,  sold  at  8f% 
discount. 

11.  What  is  the  selling  price  of  17  shares  of  stock  at  a  dis- 
count of  3f  %  ? 

12.  A  paid  14 J%  premium  on  66  shares    of    mining    stock. 
What  did  the  stock  cost  him  ? 

IS.  I  sold  through  a  broker  45  shares  of  Wabash  stock  at 
SJ%  discount,  brokerage  \%.  What  amount  did  I  receive? 

14-  B's  broker  bought  15  shares  of  railroad  stock  at  a  dis- 
count of  19%,  and  charged  f%  for  buying.  How  much  did  the 
stock  cost  B  ? 

15.  Lyman  bought  18  shares  of  stock  at  5%%  discount   and 
sold  them  at  13%  premium.    How  much  did  he  gain  by  the  trans- 
action ? 

16.  I  purchase  30  Chicago  city  5's  at%5%   discount.     How 
much  less  than  the  face  did  I  pay  for  the  bonds? 

17.  A  purchased  through  his  broker  18  U.  S.  4's  at  122|, 
brokerage  \%.     How  much  more  than  the  face  did  he  pay  for 
the  bonds? 

18.  If  Cook  County  bonds  are  selling  at  93,  what  is  the  dis- 
count and  selling  price  of  $3600  of  the  bonds? 

19.  Find  the  proceeds  of  the  following  bonds  allowing  \% 
brokerage;  100  U.  S.  4£'s  of  1891  at  103f ;  75  Chicago  6's  of 
1890  at  103£;  125  P.  Ft.  W.  R.  R.  ($50),  bonds  at  44^. 

20.  My  broker  bought  for  me  38  shares  of  bank  stock  at  92, 
and  sold  the  same  for  103.    He  charged  \%  for  buying  and  selling. 
How  much  did  I  gain  ? 

21.  Brown  bought  through  a  broker  52  shares  of  stock    at 
16%  discount.     He  paid  an  assessment  of  4%  and  then  sold  at 
98.    How  much  did  he  gain,  the  brokerage  being  \%  for  buying? 

22.  A  broker  bought  on  his  own  account  93  shares  of  I.  C. 
R.  R.  stock  at  95  J.     He  received  a  dividend  of  5%,    and    then 
sold  his  stock  at  a  premium  of  6%.    Find  his  gain. 


STOCKS    AND    BONDS  278 

23.  Find  the  cost  of  the  following  bonds  allowing  f  %  broker- 
age:  35  U.  S.  4's  of  1907  at  123f ;  80  Chicago  4J's  of  1900  at 
107'i;  25  Cook  County  5's  of  1895  at  103J;  60  Western  Union 
Telegraph  G's  of  1911  at  87§. 

24-  I  bought  35  Illinois  state  bonds  at  84,  and  sold  them  at 
105  after  having  received  3%  interest.  What  was  my  whole 
gain,  and  rate  of  interest  on  the  investment? 

25.  How  many  shares  of  stock  does  a  man  own  whose  divi- 
dend is  $4G8,  the  rate  of  dividend  being  6%  ? 

NOTE.— Since  6%  =  $468,  1%  will  =  $78,  and  100%  =  $7800. 

26.  N.  W.  R.  R.  stock  is  selling  at  5%  above  par.     How 
many  shares  does  a  man  buy,  who  pays  $135    more    than    par 
value  ? 

27.  The  dividend  was  $198  and  the  rate  of  dividend  was  6%, 
find  the  par  value. 

28.  I  receive^  a  dividend  of  $348.50.     The  rate  of  dividend 
was  8J%.    Find  the  number  of  shares  I  own. 

29.  An  assessment  of  3f%  was  $47.25,  find  the  par  value. 

30.  A  dividend  at    2$%    was    $210.      What    is    the    market 
value  of  the  stock  at  a  premium  of  22%? 

31.  A  speculator  paid  $259  premium  on  stock  that  sold  at  7% 
above  par.     He  sold  the  stock  at  a  gain  of  9%.     Wrhat  did  he 
receive  for  it? 

32.  A  broker  bought  C,  B.  &  Q.  R.  R.  bonds  at  93J,  and 
paid  $1350  less  than  the  face  of  the  bonds.     How  many  bonds 
did  he  buy  and  what  did  they  cost  ? 

33.  Bought  at  107J,  Cook  County  bonds  and  paid,  including 
\%  brokerage,  $1125  more  than  the  face  of  the  bonds.     How 
many  $50  bonds  did  I  buy? 

34.  B  paid  $21593.75  for  25  $1000  U.  S.    4f  s.     What    was 
the  quotation  of  the  bonds  ? 

NOTE. — Divide  the  market  value  by  the  par  value. 

35.  A  speculator  paid  $4284.50,  including  brokerage  \%,  for 
38  C.  M.  &  St.  P.  G's  of  1910.     What  was  the  quotation  of  the 
bonds  ? 

18 


274  NEW   BUSINESS   ARITHMETIC 

36.  A  paid  $360  premium  on  45  $100  U.  S.  4J's.    What  was 
the  rate  of  premium? 

37.  How  many  U.  S.  4's  of  1907  of  $50  each  at  97,    can   be 
bought  for  $2917.50,  allowing  i%  brokerage? 

38.  What  is  the  face  value  of  U.  S.  4J's,  that  cost  $19088.75 
at  103 J,  brokerage  •§%  ? 

39.  I  paid  $3315  for  Chicago  5's  at  10£%  premium      How 
many  $50  bonds  did  I  buy? 

40.  How  many  $25  bonds  can  be  bought  for  $1254.50  at  3f  % 
discount,  brokerage  -|%  ? 

41.  Jones  sold  15  $100  R.  R.  4's  at  15%  above  par,  and  in- 
vested proceeds  in  mining  stock  at  13f  %  discount.     How  many 
$50  shares  of  the  latter  did  he  receive  ? 

42.  What  is  the  rate  per  cent,  on  investment,  if  U.  S.  4's  are 
purchased  at  125? 

43.  What  rate  will  I  receive  on  my  investment,  if  I  invest 
$2940  in  Cook  County  5's  at  98  ? 

44-  State  5's  are  purchased  at  124-%  premium.    What  rate  is 
realized  on  the  investment? 

45.  I  invested  $2175  in  city  5's  at  87,  I  sold  the  same  at  92J 
after  receiving  the  interest  for  one  year.    What  was  my  gain  and 
rate  of  income  on  investment? 

46.  Bought  U.  S.  4J's  at  107J.    I  sold  same  at  10%  premium 
after  receiving  three  quarterly  payments  of  interest.     What  was 
the  rate  of  income  on  the  investment  ? 

47.  I  invested  $3440  in  U.  S.  4f  s  at  107J,  $2694  in  U.  S.  4's 
at  112J  and  $4116  in  Illinois  6's  at  85J.     What  was  my  annual 
income,  and  rate  per  cent,  on  investment? 

48.  Which  is  the  more  profitable  investment,  a  stock  at  125, 
paying  8%  annually,  or  a  bond  at  90,  paying  6%  annually? 

49.  Three  companies,  A,  B  and  C,  are  to  be  consolidated  on 
the  basis  of  the  relative  market  values  of  their  stock. 

Thus,  A's  capital  $1,000,000,  market  value  100%  ; 
B's  capital  $1,500,000,  market  value  50%  ; 
C's  capital      $625,000,  market  value  40% 
The  capital  of  the  consolidated  company  is  to  be  $2,000,000, 


STOCKS    AND    BONDS 


275 


in  20000  shares  of  $100  each.  What  proportion  and  what  amount 
of  the  capital  should  be  allotted  to  each  of  the  old  companies; 
and  how  much  stock  in  the  new  company  should  the  holder  of  1 
share  of  the  stock  of  each  of  the  old  companies  be  entitled  to  ? 

50.  When  3%  government  bonds  are  quoted  at  101,  what  sum 
must  be  invested  to  yield  an  income  of  $810  a  year? 

51.  Bought  October  12th,  400  Pacific  Mail  at  42 J,  and  200 
Michigan  Central  at  92J;  November  10  sold  the  former  at  42}, 
and  the  latter  at  92|;  what  was  my  gain  not  considering  interest? 

52.  Which  would  be  the  better  investment,  $12120  in  N.  J. 
Central  at  80,  paying  3%  annual  dividends,  or  the  same  invested 
in  Chemical  Bank  stock  at  2020,  paying  15%  every  2  months? 

53.  A  customer  deposited  $500  margin  with  a  broker  Novem- 
ber 23,  who  purchased  for  him  50  shares  Michigan  Central  at  80. 
He  sold  the  same  stock  November  30  at  98 ;  what  was  the  gain, 
brokerage  \%t 

STATEMENT 


Nov.  23. 
Nov.  30. 

Nov.  23. 
Nov.  30. 

Nov.  30. 

Dr. 
To  50  sh.  Mich.  Cen.  at  80.  .  .  $4000 
Brokerage  Vs  %  6.25 

4006 

* 

25 
** 

51=*** 

** 

Int.  on  $4006.25,  7  days  at  6#  ........ 

Cr. 
Bv  margin  deposited 

500 

**** 

*# 
** 

**#* 

**_ 

By  50  sh.  Mich.  Cen.  at  98.  ...  $**** 
Less  Brokerage  Vs%  

Int.  on  $500,  7  days  

Balanc 
Less  r 
Gain.  . 

e       .  • 

**** 

500 
*** 

** 
*# 

nargin 

NOTE. — The  brokerage,  ^  of  1%  is  equal  to  $12.50  on  100  shares  of 
stock  at  the  par  value  of  $100  each. 

54.  July  10  deposited  with  my  broker  $800  margin  for  pur- 
chasing 60  shares  Mo.  Pacific  R.  R.  stock  at  92J.    The  stock  was 
sold  July  28  at  95|.     Allowing  6%  interest  on  the    deposit   and 
charging  6%  interest  on  the  purchase  and  1%  brokerage.    What 
was  my  net  profit? 

55.  If  a  certain  stock  yields  a  dividend  of  15%  per  annum, 
what  is  its  value  when  money  is  worth  8%  ? 


276  NEW   BUSINESS   ARITHMETIC 

56.  On  May  7,  I  deposited  with  my  broker  $2000  margin, 
and  instructed  him  to  buy  stocks.     The  same  day  he  bought  for 
my  account  300  shares  N.  Y.  Central  at  118J.    He  sold  the  stock 
May  26,  at  122|.     Interest  6%,  brokerage  \%.     What  was  my 
gain? 

57.  June  14,  I  "margined"  $2000  and  sold  "short"  through 
my  broker  200  shares  Mich.  Cen.  at  90  and  June  28  "covered" 
my  "short"  at  86f.     Brokerage,  |%.     Int.,  6%.     Find  gain.* 

58.  A  speculator  deposited  with  his  broker  $800  margin  April 
16,  who  purchased  40  shares  B.  &  O.  at  114f.    He  sold  the  stock 
June  5  at  118f ;  find  gain  or  loss,  interest  6%,  brokerage  J%. 

59.  A  capitalist  received  his  quarterly  interest  on  4.%%  bonds 
amounting  to  $38.2.50  and  then  sold  the  same  at  105J.     What 
were  the  net  proceeds  of  the  sale,  brokerage  %%? 

GO.  On  July  10,  I  deposited  with  my  broker  $1200  margin 
with  directions  to  buy  Western  Union  stocks.  The  same  da}-  he 
purchased  for  my  account  200  shares  Western  Union  at  116J.  He 
sold  the  stock  August  16  at  112^.  Interest  1%,  brokerage  1%. 
What  was  my  loss  ? 

61.  If  stock  actually* worth  $88  per  share  be  watered  by  issu- 
ing a  stock  dividend  of  10%,  what  is  the    actual    value    of    the 
watered  stock  ? 

62.  An  investor  owned  the  following  list  of  securities : 

NATURE  PAR  VALUE      COST        RATE 

Bank  Stock,  $2500  190  8% 

Personal  Note,  1400  Par  6% 

Personal  Note,  500  Par  6% 

Real  Estate  Mortg.,     1800  Par  6% 

Elec.  Ry.  Bonds,  1000  99}  5% 

Gas  Bonds,  3000  100  5% 

What  was  his  per  cent,  of  income  on  the  entire  investment 

considered  as  one?     What  was  his  per  cent,  of  income  on  his 

investment  in  the  bank  stock  ?    What  was  the  total  investment  ? 


*  It  is  not  a  general  custom  among  brokers  to  allow  interest  on 
margins  advanced  for  "short"  sales,  but  it  is  sometimes  done  and  problem 
57  is  to  be  solved  on  this  basis. 


EXCHANGE 

404.  Exchange  is  a  method  of  making  payments  between 
persons  in  different  cities  by  means  of  drafts. 

If  a  party  in  Chicago  desires  to  remit  a  sum  of  money  to  a  party  in 
New  York,  he  buys  of  a  Chicago  bank  a  draft  on  a  New  York  bank  and 
sends  it  to  the  party  in  New  York.  The  New  York  party  indorses  the  draft 
and  presents  it  for  payment  to  the  bank  on  which  it  is  drawn,  either  di- 
rectly or  through  some  other  bank. 

405.  Domestic   Exchange   or   Inland   Exchange   is   the   ex- 
change between  places  in  the  same  country. 

406.  Foreign  Exchange  is  the  exchange  between  places  in 
different  countries.    A  foreign  draft  is  called  a  Bill  of  Exchange. 

407.  Exchange  is  At  Par  when  the  cost  of  a  draft  equals  its 
face ;  above  par  or  at  a  premium,  when  the  cost  of  a  draft  exceeds 
its  face ;  and  below  par  or  at  a  discount  when  the  cost  of  a  draft 
is  less  than  its  face. 

Time  drafts  or  bills  of  exchange  are  subject  to  bank  discount  on  their 
face  value  for  the  time  specified. 

An  Acceptance  is  the  written  promise  of  the  Drawee  to  pay  the  draft 
when  due.  A  Draft  is  accepted  by  the  Drawee's  writing  across  its  face  the 
word  "Accepted"  followed  by  the  date  of  the  acceptance  and  his  signature. 

408.  The  Balance  of  Trade  between  two  places  or  countries 
is  the  difference  between  the  amounts  which  each  owes  the  other. 

Thus  if  the  banks  of  New  York  owe  the  banks  of  London  $40,000,000 
and  the  banks  of  London  owe  the  banks  of  New  York  $35,000,000,  the 
balance  of  trade  is  $5,000,000  against  New  York  and  in  favor  of  London. 

409.  The  Course  of  Exchange  between  two  places  is  the  price 
paid  at  one  place  for  drafts  on  the  other.    The  course  of  exchange 
is  above  or  below  par,  according  as  the  balance  of  trade  is  against 
or  in  favor  of  it. 

A  person  may  properly  remit  money : 

1.  By  sending  a  Post  Office  money  order  or  express  money  order,  for 
small  amounts.  These  are  in  effect  drafts,  but  are  sold  at  schedule  prices, 
and  not  on  principles  of  percentage. 

277 


278  NEW   BUSINESS   ARITHMETIC 

2.  By  sending  the  actual  money  by  express  or  otherwise. 

3.  By  remitting  a  draft  drawn  on  any  bank  in  the/  city  where  the 
money   is  payable   or  some  place  that  is   recognized  as   a  center  of   ex- 
change. 

New  York  is  the  recognized  center  of  financial  transactions  in 
the  United  States  as  London  is  of  the  world. 

DOMESTIC  EXCHANGE 

410.  Domestic  Exchange  relates  to  payments  between  cities 
of  the  same  country. 

Computations  in  exchange  are  based  upon  the  principles  of 
percentage  and  embrace  four  quantities,  viz. :  Face  of  Draft  = 
Base;  Rate  of  Exchange  =  Rate;  Premium  or  Discount  =  Per- 
centage; Cost  of  a  Draft  =  Amount  or  Difference. 

ORAL  PROBLEMS 

1.  Find  the  exchange  at  \%  premium  on  the  following  drafts: 
$640,  $720,  $400,  $320. 

2.  Find  the  exchange  at  \%  discount  on  the  following  drafts : 
$200,  $300,  $400,  $3000. 

3.  What  will  the  following  drafts  cost  at  a  premium  of  \%  : 
$200,  $1500,  $250. 

4.  Find  the  cost  of  the  following  drafts  at  a  discount  of  \%  : 
$80,  $250,  $320,  $480,  $75. 

5.  I  buy  a  bill  of  goods  amounting  to  $200,  if  cash  is  paid  at 
once  a  discount  of  10%  will  be  aHowed.     I  at  once  buy  a  bank 
draft  at  a  premium  of  \%.    What  do  the  goods  cost  me? 

WRITTEN   PROBLEMS 

1.  Find  the  cost  of  a  draft  for  $560  at  \%  premium. 

2.  Find  the  cost  of  a  draft  for  $725  at  \%  premium. 

3.  Find  the  cost  of  a  draft  for  $1316  at  f  %  discount. 

4.  Find  the  cost  of  a  draft  for  $1867.50  at  \\%  discount. 

5.  Find  the  cost  of  a  draft  for  $620  at  \\%  premium. 

6.  Find  the  cost  of  a  draft  for  $2860  at  \\%  discount. 

7.  A  merchant  in  Boston  bought  a  draft  on  Detroit  at  %%  dis- 
count.   If  the  face  was  $290,  what  was  the  cost  of  the  draft? 


EXCHANGE  279 

S.  I  remit  a  draft  of  $480  to  B  on  account,  the  rate  of  ex- 
change being  \%  premium.  What  was  the  cost? 

9.  I  owed  Lyman  of  Hartford  $250.  He  allowed  me  a  dis- 
count of  10%,  and  I  remitted  a  draft  in  payment.  Find  cost  of 
the  draft  at  \%  discount. 

10.  Brown  bought  20  shares  stock  at  93,  and  paid  for  same 
by  draft  at  f%  premium.    How  much  did  the  draft  cost  him? 

11.  I  sent  a  draft  to  my  agent  to  buy  1200  bu.  of  wheat  at  75 
cents  per  bu.,  at  3%  commission.     I  paid  \%  premium  on  the 
draft.    What  was  the  cost  ? 

12.  A  retail  merchant  bought  a  bill  of  $684  on  3  months'  time, 
or  10  and  5%  off  for  cash.     He  accepted  the  cash  offer  and  re- 
mitted in  payment  a  draft  at  f  %  premium.    What  did  the  goods 
cost  him? 

IS.  Find  the  face  of  a  draft  that  cost  $875  at  \\%  premium. 

NOTE.— Since  a  draft  for  $1  cost  $1.01*4  $875  will  buy  as  large  a  draft 
as  $1.01^4  is  contained  times  in  $875. 

11+.  Find  the  face  of  a  draft  that  cost  $325.60  at  \%  discount. 

15.  Find  the  face  of  a  draft  that  cost  $1275.60  at  \\%  pre- 
mium. 

16.  Find  the  face  of  a  draft  that  cost  $329.45  at  2%%  pre- 
mium. 

11.  A  merchant  paid  $932.40  for  a  draft  on  Nashville  at  %% 
premium.  Find  the  face  of  the  draft. 

18.  The  cost  of  a  draft  at   \\%   discount  on  Albany  was 
$364.45.    What  was  the  face  of  the  draft? 

19.  A  sight  draft  on  St.  Louis  cost  $459.42  at  \\%  discount. 
For  what  sum  was  the  draft  drawn? 

20.  What  is  the  cost  of  a  draft  for  $1200  on  Omaha  for  60 
days  at  \%  discount,  interest  at  8%  ? 

NOTE.— Proceeds  of  $1  for  60  da.  at  8%  =  $.986|  —  $.005  discount  = 
$.981|,  cost  of  a  draft  for  $1.  A  draft  for  $1200  will  cost  1200  times  as 
much. 

21.  Find  the  cost  of  a  75-day  draft  drawn  on  Pittsburg  for 
$1860.    The  rate  of  exchange  is  \%  premium  and  interest  6%. 


280  NEW   BUSINESS   ARITHMETIC 

22.  I  remitted  to  a  creditor  a  draft  for  $275  at  £%  discount. 
The  draft  was  at  15  days'  sight,  interest  6%.    Find  cost. 

23.  Davis  remitted  a  45-day  draft  in  payment   of    a    bill    of 
$5760;  the  exchange  was  f%  premium  and  interest  5%.     What 
did  he  pay  for  the  draft? 

24.  What  is  the  cost  of  a  draft  for  $6840,  drawn  at  27  days 
on  Albany,  if  the  exchange  is  %%  discount  and  interest  6%? 

25.  How  much  must  I  pay  for  a  draft  of  $340  on  Boston  for 
51  days  at  \%  discount,  if  money  is  worth  10%  ? 

26.  B  sold  me  a  horse  that  cost  him  $120,  at  13J%  gain;  I 
paid  for  same  with  a  New  York  draft  at  \%  discount,  for  69  days 
at  1%  interest.    What  was  the  net  cost  of  the  horse  to  me? 

27.  I  bought  a  draft  drawn  on  Boston  for  18  days  at  -£$%  dis- 
count.    How  much  did  the  draft  cost  me,    the    face    being    for 
$1238.40,  and  money  loaning  at  6%  interest? 

28.  A  grain  dealer  bought  wheat  at  90  cents  per  bushel,  and 
remitted  for  same  a  Chicago  draft  bought  for  $1344.60  at  \%  dis- 
count.   How  many  bushels  of  wheat  did  he  buy  ? 

29.  I  paid  $475.80  for  a  bank  draft  at  1%  discount,  to  send  a 
wholesale  merchant  for  a  bill  of  goods  bought  at  a  discount  of  6% 
from  the  invoice  price.     Find  the  invoice  price. 

SO.  A  paid  $584.70  for  a  New  Orleans  draft  at  \\%  discount 
for  60  days,  interest  6%.  Find  the  face  of  the  draft. 

31.  A  merchant  bought  a  15-day  draft  for  $961.50.     What 
was  the  face  of  the  draft,  if  exchange  was  If  %  premium  and  in- 
terest 4%  ? 

32.  The  cost  of  a  New  York  draft  at  \\%  premium,  for  105 
days  was  $433.40.    What  was  the  face  of  the  draft,  money  being 
worth  5%? 

33.  A  60-day  draft  at  If  %  discount  was  remitted  for  payment 
of  potatoes  bought  at  a  gain  of  10%  to  the  seller.    What  did  the 
goods  cost  the  seller,  the  draft  costing  $117.30  at  6%  ? 

34-  When  exchange  was  at  \%  discount,  and  money  loaning 
at  8%,  Lyman  paid  $1773.30  for  a  Chicago  draft,  drawn  at  33 
days'  sight.  What  would  the  draft  cost  him,  if  exchange  was  at 
%%  premium? 


EXCHANGE  281 

35.  I  bought  mining  stock  at  31%  discount,  and  remitted  in 
payment  a  bank  draft  at  If  %  premium,  that  cost  $1380.  How 
many  shares  did  I  buy,  the  time  of  the  draft  being  72  days  and 
interest  at  7%? 

FOREIGN  EXCHANGE 

411.  Foreign  Drafts  or  Bills  of  Exchange  are  usually  ex- 
pressed in  the  money  of  the  country  on  which  they  are  drawn. 

Drafts  drawn  on  persons  and  banks  located  in  England,  Ireland  and 
Scotland,  are  expressed  in  pounds,  shillings  and  pence ;  on  France,  Bel- 
gium or  Switzerland  in  francs ;  on  Germany,  in  marks,  etc. 

412.  The  Par  of  Exchange  is  the  value  of  the  money  of  one 
country  expressed  in  the  denominations  of  another. 

1.  The  intrinsic  par  of  exchange  is  the  value  of  the  coin  of  one 
country  in  the  coin  of  another,  based  upon  the  relative  weight  and 
fineness  of  the  two  coins. 

2.  The  commercial  par  of  exchange  is  the  market  value  of  the 
currency  of  one  country  as  compared  to  that  of  another. 

413.  Foreign  bills  of  exchange  are  usually  drawn  at  sight 
or  sixty  days  after  sight.     The  former  are  known  as  short  ex- 
change, and  the  latter  as  long  exchange. 

Days  of  grace  are  usually  allowed  on  all  foreign  exchange. 

The  course  of  exchange  on  time  bills  is  as  much  less  than  that 
on  sight  bills  as  the  per  cent,  of  interest  for  the  time  given  plus 
the  days  of  grace. 

414.  A  Documentary  Bill  of  Exchange  is  one  accompanied 
with  a  Bill  of  Lading  and    Insurance  Certificate,  giving  the  title 
of  the  property  represented  by  the  Bill  of  Lading  to  the  holder  of 
the  Bill  of  Exchange. 

415.  The  following  quotations  of  Foreign  Exchange  were 
taken  from  a  newspaper. 

STERLING  EXCHANGE SIXTY  DAYS.  .    SIGHT 

Posted  Rates. 4.85^ 4.89 

Actual  Rates 4.85 4.88^ 

Documentary  Bills 4.82^4.83^4 4.85^@4.86}4 

FRENCH  EXCHANGE SIXTY  DAYS SIGHT 

Posted  Rates 5.18^ 5.16*4 


282  NEW   BUSINESS   ARITHMETIC 

Documentary  Bills  ..............  5.22^  ....................  .........  .5.20 

GERMAN  EXCHANGE  ..............  SIXTY  DAYS  ......................  SIGHT 

Posted  Rates  ....................  95>4 

Documentary  Bills  ..............  94@94}4 

NOTES.—  1.  Sterling  Bills  at  4.82^@4.83^  means  that  the  lowest  price 
paid  on  that  day  was  $4.82^4  for  one  £,  and  the  highest  $4.83^4. 

2.  French  Exchange  at  5.18^4  means  that  the  price  was  5.18^4  francs 
for  $1.  Quotations  are  sometimes  given,  showing  the  cost  of  a  franc,  as, 


3.  German  Exchange  at  94@94^4  means  that  the  lowest  price  was 
$.94  for  four  marks;  and  the  highest  $.94*4.  Quotations  are  sometimes 
given,  showing  the  cost  of  a  mark  ;  as  $.237. 

1.  What  sum  must  I  pay  for  a  draft  of  £890  on  London,  ex- 
change at  $4.86}? 

2.  James  Smith  remits  to  a  customer  a  draft  on  Paris  for  4056 
francs,  when  exchange  is  5.20.    Find  the  cost. 

3.  Geo.  Graham  bought  a  draft  of  2740  marks,  to  pay  for  a 
bill  of  goods.    What  did  it  cost  at  96f  ? 

4.  A  merchant  sold  to  a  bank  a  draft  of  £320.8s.  6d.  at  $4.82J. 
How  much  did  he  receive  for  it?  (See  footnote,  page  283.) 

5.  A  commission  merchant  remitted  to  his  principal  a  draft 
of  1935  francs  at  5.16.    Find  the  net  proceeds  of  the  sale. 

6.  I  received  from  my  agent  a  draft  of  1975J  marks  at  94£. 
What  was  the  amount  of  sale,  commission  being  5%  ? 

7.  An  agent  received  a  draft  of  £1245.  2s.  3d.  to  invest  in 
grain  at  2%  commission.    How  much  can  he  invest,  exchange  at 
$4.84  J? 

8.  William  Brown  bought  a  bill  of  goods  at  a  discount  of 
20%,  and  remitted  for  same  a  draft  for  3209|  francs  at  5.12J. 
Find  the  invoice  price  of  the  goods. 

9.  C.  H.  Fuller  received  a  draft  for  8400  marks  to  invest  in 
wheat  at  85  cents  per  bu.,  at  5%  commission.    How  many  bush- 
els did  he  buy,  exchange  being  93  J  ? 

.10.  My  broker  drew  on  me  for  £276|f  for  stock  bought  at  110. 
What  was  the  purchase  price  of  the  stock,  if  the  brokerage  was 
2%,  and  exchange  $4.86? 


EXCHANGE  283 


11.  I  remitted  a  draft  on  a  Paris  bank  for  3072  francs  at  5. 
in  payment  of  a  lot  of  silk  bought  at  a  discount  of  20  and 
Find  the  invoice  price. 

12.  D.  W.  Graham  remitted  to  his  principal  a  draft  for  8000 
marks,  bought  at  96,  for  a  lot  of  goods  sold  at  4%  commission. 
Find  the  amount  of  his  commission. 

13.  What  is  the  face  of  a  draft  on  a  Liverpool  bank,  that  cost 
$2848.09,  exchange  at  $4.88  ? 

14.  What  is  the  face  of  a  draft  on  a  Lyons  bank,  that  cost 
$812,  exchange  at  5.16^  francs  to  $1? 

15.  The  cost  of  a  draft  on  Berlin  was  $156.75,  when  exchange 
was  $.95  for  4  marks.    Find  face  of  the  draft. 

16.  James  Nolan  paid  $3439.95  for  a  draft  on  a  bank  of  Dub- 
lin, exchange  at  $4.84J.    What  was  the  face  of  the  draft? 

17.  An  agent  sold  goods  for  a  merchant  of  Berlin  at  6%% 
commission.    What  is  the  face  of  the  draft  he  must  send  in  pay- 
ment, exchange  at  $.93  J;  if  the  amount  of  the  sale  was  $2000? 

18.  What  is  the  face  of  a  draft  on  London,  that  will  pay  for 
an  invoice  of  $4000,  bought  at  a  discount  of  25  and  14§%  ;  when 
exchange  is  $4.86^? 

19.  I  paid  $368  for  a  draft  on  Paris,  exchange  at  5.17},  to  re- 
mit in  payment  for  cloth  sold  at  8%  commission.    Find  my  com- 
mission and  the  face  of  the  draft. 

20.  A  merchant  paid  $720  for  a  draft  on  Frankfort,  when  ex- 
change was  94,  to  remit  in  payment  for  cloth  that  was  bought  at 
3  marks  per  yard.    How  many  yards  did  he  buy  ? 

To  reduce  English  money  to  the  decimal  of  a  pound  • 

(a)  Write  the  number  of  pounds. 
(6)  Place  a  decimal  point  after  this. 

(c)  Divide  the  number  of  shillings  by  2  and  write  the  result  as 
tenths  of  a  pound. 

(d)  Multiply  the  number  of  pence  by  4|  and  write  the  result  as 

thousandths  of  a  pound. 


BANKS  AND   BANKING 

416.  A  Bank  is  an  institution  which  deals  in  money  or  its 
representative.     Banks   are   usually   incorporated   concerns,   and 
are  either  National  or  State  banks. 

The  chief  business  of  a  bank  consists  in : 

1.  Receiving  deposits  of  money   for  safe  keeping  and  conve- 

nience of  customers. 

2.  Loaning  money  by   discounting  and   collecting   commercial 

paper. 

3.  Issuing  bills  or  notes  as"  a  circulating  medium. 

4.  Making  collections. 

5.  Selling  drafts  on  its  correspondents. 

Banks  make  no  charge  for  keeping  deposits  and  pay  no  interest  on 
them  except  in  rare  cases,  and  then  at  a  low  rate.  The  privilege  of 
loaning  out  a  large  proportion  of  the  deposits  is  a  source  of  profit  to  the 
bank,  sufficient  to  compensate  it  for  keeping  the  account. 

NATIONAL  BANKS 

417.  A  National  Bank  is  one  which  is  organized  under  the 
National  Banking  Act  of  the  United  States. 

According  to  the  National  Banking  Act,  Banking  Associa- 
tions may  be  formed  of  any  number  of  persons  not  less  than  five. 

No  association-  can  be  organized  with  a  capital  less  than 
$100,000,  except  in  cities  whose  population  does  not  exceed 
6,000,  where  they  may  be  formed,  with  the  approval  of  the 
Secretary  of  the  Treasury,  with  a  capital  of  $50,000 ;  also  except 
that  the  Secretary  may  permit  the  organization  of  a  bank  with 
a  capital  of  not  less  than  $25,000  where  the  population  does 
not  exceed,  3,000.  In  cities  the  population  of  which  exceeds 
50,000,  the  capital  must  not  be  less  than  $200,000,  the  stock 
being  divided  into  shares  of  $100. 

All  national  banks  are  subject  to  periodical  visitation  and 
examination  by  the  National  Bank  Examiner,  as  the  represent- 
ative of  the  Secretary  of  the  Treasury. 

284 


BANKS    AND    BANKING  285 

The  stockholders  of  national  banks  are  liable  individually 
beyond  their  investment  for  the  debts  of  the  bank,  to  an  amount 
equal  to  the  stock  which  they  hold. 

National  banks  are  not  allowed  to  loan  money  on  real  estate 
security,  and  real  estate  purchased  or  mortgaged  to  secure  a 
previous  debt  must  be  disposed  of  within  five  years. 

418.  Circulation.    National    banks    issue    circulating    notes 
by    depositing   as    security    with    the   United    States    Treasurer 
an  amount  of  Registered  Bonds  not  less  than  one-fourth  of  the 
capital  paid  in.     These  bonds  are  held  as  security  for  the  circu- 
lating notes,  and  in  case  the  bank  should  fail  the  Government 
will  redeem  the  notes.     Banks  are  allowed  to  issue  circulating 
notes  to  the  full  amount  of  the  par  value  of  the  bonds  deposited, 
but  no  bank  can  have  a  circulation  greater  than  the  amount  of 
the  capital  stock  paid  in. 

A  bank  desiring  to  reduce  its  circulating  notes  may  deposit 
with  the  Treasurer  legal  tenders  or  specie  in  amounts  not  less 
than  $9,000,  and  withdraw  a  proportionate  amount  of  the  bonds 
previously  deposited.  However,  the  amount  of  bonds  on  deposit 
shall  not  be  reduced  below  $50,000. 

419.  Xational  Bank  Notes    are    redeemable    by    the    banks 
issuing  them  or  by  the  Treasurer  of  the  United  States. 

Every  national  bank  is  required  to  keep  on  deposit  in  the 
Treasury  of  the  United  States,  a  sum  equal  to  5  per  cent,  of  its 
circulation  for  the  purpose  of  redeeming  its  bills,  which  is 
counted  in  as  part  of  the  Reserve. 

420.  A  Reserve  Fund  equal  to  25  per  cent,  of  their  deposits 
is  required  to  be  kept  by  national  banks  in  the  cities  of  New 
York,     Boston,     Philadelphia,     Albany,     Baltimore,     Pittsburg, 
Washington,    New    Orleans,    Louisville,    St.    Louis,    Cleveland, 
Detroit,   Chicago,   Milwaukee   and   San    Francisco,   and    15   per 
cent,  by  all  other  national  banks. 

These  are  called  Reserve  Cities,  and  the  excess  above  the 
requirements  is  called  the  Surplus  Reserve. 

421.  A  Surplus  Fund,  of  the  net  earnings  of  the  bank,  is 
also  required  by  law   to  be   set  aside,  before  the  usual  semi- 
annual dividends  are  declared,  consisting  of  one-tenth  of  the  net 


28G  NEW  BUSINESS   ARITHMETIC 

profits  for  the  preceding  half  year,  until  this  fund  amounts  to 
20  per  cent,  of  the  capital. 

£22.  A  Tax  of  one-half  of  1  per  cent,  each  half  year  is  paid 
to  the  United  States  by  national  banks  on  the  average  amount  of 
their  circulation.  But  if  the  redemption  bonds  bear  but  2%  the 
tax  is  one-fourth  of  \%  each  half  year. 

The  advantage  to  a  bank  under  the  National  Bank  Act  is  that  it 
receives  interest  upon  the  bonds  deposited  with  the  Treasurer  and  also 
loans  and  uses  its  circulating  notes,  and  thereby  derives  a  profit  from 
them — thus  making  a  double  income  upon  the  same  amount  of  capital, 
while  paying  a  tax  upon  the  circulation  and  being  exempt  from  a  tax  on 
the  bonds. 

A  bank  desiring  to  go  into  liquidation  must  deposit  with  the 
Treasurer,  six  months  before  such  liquidation,  an  amount  of  lawful 
money  equal  to  its  outstanding  circulation. 

The  law  also  requires  that  a-  sufficient  amount,  thus  deposited  for 
the  payment  of  circulating  notes,  must  remain  in  the  Treasury  until  the 
last  outstanding  note  shall  have  been  presented.  Hence,  it  will  be  seen 
that  the  Government  derives  the  benefit  from  notes  which  are  lost  or 
destroyed  by  fire  and  water. 

PROBLEMS 

1.  A  bank  having  a  paid  up  capital  of  $250000    desires    to 
issue  circulating  notes.     What  is  the  smallest  amount  of  bonds 
that  it  can  deposit  as  security  for  such  notes,  and  what  amount 
of  notes  will  it  receive  ? 

2.  It  is  desired  to  organize  a  national  bank  in  a  city  whose 
population  is  3865.    How  many  persons  and  what  amount  of  cap- 
ital are  necessary?     What  amount  of  circulating  notes  may  the 
bank  issue? 

3.  A  bank  deposits  bonds  to  the  amount  of  $480000  with  the 
Treasury.     What  will  be  the  amount  of  its  circulating  medium? 
What  is  the  amount  of  its  redemption  fund? 

4.  A  national  bank  having  a  capital  of  $400000,  by  injudi- 
cious loans,  impairs  its  capital  $125000.    What  per  cent,  may  each 
stockholder  be  assessed  to  make  good  the  loss?     What  must  A 
pay  who  owns  5  shares  of  stock  ? 

5.  A  bank  located  in  a  reserve  city  has  deposits  amounting  to 
$850260.    What  is  the  amount  of  its  reserve  fund? 

6.  A  national  bank  with  a  capital  of  $600000,  and  having  a 


BANKS    AND    BANKING  287 

surplus  of  less  than  20%  of  its  capital  earns  $22350  net  profits 
during  six  months.  What  amount  must  be  carried  to  the  sur- 
plus fund  and  what  amount  will  remain  after  declaring  a  3% 
semi-annual  dividend? 

7.  What  is  the  redemption  fund  of  a  bank  having  a  circula- 
tion of  $425000?    What  amount  of  bonds  were  deposited  to  se- 
cure this  circulation  ? 

8.  Find  the  semi-annual  tax  on  a  bank  having  an  average  cir- 
culation of  $128650  if  3%  bonds  were  deposited  to  secure  circu- 
lation. 

9.  A  national  bank  having  a  capital  of  $500000  and  a  surplus 
fund  of  $65000,  earned  $32650  during  six  months.    What  amount 
will  be  carried  to  the  surplus  fund?     What  amount  will  remain 
after  declaring  a  semi-annual  dividend  of  3%%  ? 

10.  A  bank  desiring  to  reduce  its  circulation  deposited  with 
the  Treasurer  $51400  in  specie.  What  was  the  market  value 
of  the  bonds  withdrawn  at  108J? 

SAVINGS  BANKS 

423.  A  Savings  Bank  is  an  institution  which  receives  de- 
posits of  money  for  safe  keeping,  and  allows  depositors  interest 
thereon. 

424.  Interest  is  usually  credited  on  deposits  twice  each  year 
—July    1   and  January   1,   although   some   banks   credit   the   in- 
terest quarterly.     If  the  interest  is  not  withdrawn  it  is  allowed 
to  draw  interest,  and  thus  the  interest  is  compounded. 

Usually  no  interest  is  allowed  on  parts  of  a  dollar,  and  that  is  the 
plan  which  will  be  followed  by  the  student.  Banks  do  not  usually  allow 
interest  on  any  sum  which  has  not  been  in  for  the  full  term  of  the  interest 
period.  Some  banks  allow  interest  on  money  which  has  been  on  deposit 
during  the  entire  quarter  previous  to  interest  day,  while  others  allow 
interest  on  sums  which  have  been  deposited  on  or  before  the  first  of  any 
month.  No  interest  is  allowed  on  amounts  withdrawn  before  interest  day. 

Savings  banks  are  subject  to  the  laws  of  the  state  in  which 
they  are  located.  In  some  states  they  are  restricted  as  to  the  size 
of  deposits,  rate  of  interest  which  they  must  allow,  etc. 

425.  Since  in  nearly  all  savings  banks  no  interest  is  allowed 
on  money  deposited  or  withdrawn  during  an  interest  term,  there- 


288  NEW   BUSINESS   ARITHMETIC 

fore,  Interest  is  computed  at  the  end  of  the  interest  term  on  the 
smallest  balance  on  deposit  at  any  time  during  the  term. 

NOTE. — If  it  is  desired  to  find  the  interest  for  several  terms,  consider 
the  interest  at  the  end  of  each  quarter  the  same  as  a  deposit  on  the  first 
day  of  the  next  quarter. 

In  the  following  examples  unless  otherwise  stated,  deposits 
draw  interest  at  4%  per  annum,  from  the  1st  of  January,  April, 
July  and  October.  Interest  days  January  1  and  July  1. 

1.  On  September  10,  A  deposited  in  a  savings  bank  $235. 
What  amount  of  interest  will  be  credited  to  his  account  on  Jan- 
uary 1  ? 

NOTE — The  deposit  will  /rot  begin  to  draw  interest  until  October  1,  and 
the  interest  at  4%  on  $235  from  October  1  to  January  1  is  $*.**. 

2.  A  depositor  is  credited  with  the  following  deposits :    Jan- 
uary 1,  1904,  $300;  June  26,  1905,  $230;  August  18,  1905,  $70. 
No  withdrawals.    What  will  be  the  credit  of  interest  on  January 
1,  1906? 

3.  On  July  1,  1902,  a  lady  deposited  in  a  savings  bank  $180 ; 
September  25,  $60;  February  10,  1903,  $140;  April  1,  $300,  and 
June  16,  $280.    What  will  be  her  credit  in  bank  January  1,  1904, 
if  no  withdrawals  have  been  made? 

4.  Mr.  C  deposits  in  a  savings  bank  which  allows  interest  at 
A%  on  deposits  from  the  first  of  each  month  and  credits  the  in- 
terest up  on  January  1  and  July  1.     His  deposits  are  as  follows : 
January  1,  1905,  $400 ;  March  16,  $130 ;  June  28,  $186 ;  August 
18,  $260.    What  will  be  his  balance  January  1,  1906? 

5.  The  following  account  is  taken  from  the  ledger  of  a  sav- 
ings bank,  that  pays   interest  at  4%   quarterly.     Interest  com- 
mences at  the  first  of  each  quarter,  viz. :    January  1,  April  1,  July 
1  and  October  1. 


BANKS    AND    BANKING 


289 


Date 

With- 
drawals 

Deposits 

Balances 

1905. 

Sept   11 

230 

230 

Oct.  30  
Xov    11      

70 

200 

30U 
500 

11)00. 
Jan   1  

500 

Jan   1 

Int  2.30 

502.30 

Jan   9 

177 

325.30 

Jan   20 

300 

25.30 

Feb  23       .... 

287 

312.30 

Mar  15       

135 

177.30 

Apr   1             .    . 

177.30 

A.pr  1 

Int     25 

177.55 

Apr  8       

75 

102.55 

Apr  20       .... 

25 

77.55 

Mav  16     

125 

202.55 

Julv  1  
Julv  1  

Int.  .77 

202.55 
203.32 

EXPLANATION. — The  in- 
terest term  being  quar- 
terly the  interest  is  added 
to  the  balance  on  the  first 
of  each  quarter.  Since 
no  interest  is  allowed  on 
money  withdrawn  during 
the  quarter,  interest  is 
computed  only  on  the 
smallest  balance  in  the 
quarter  (Art.  425).  The 
smallest  balance  in  the 
first  quarter  is  $230  and 
the  interest  on  this  for  3 
mo.  at  4%  is  $2.30.  The 
smallest  balance  during 
the  second  quarter  is 
$25.30,  the  interest  on 
which  is  $.25.  The  smallest  balance  during  the  third  quarter  is  $77.55,  the 
interest  on  which  is  $.77,  which  added  to  the  balance,  gives  the  final  balance 
as  $203.32. 

6.  January  1,  1905,  a  clerk  deposited  in  a  savings  bank  $250 ; 
January  18,  deposited  $63 ;  February  2,  withdrew  $40 ;  February 
18,  deposited  $25 ;  March  12,  deposited  $48 ;  March  18,  withdrew 
$125;  March  30,  withdrew  $175;  April  18,  deposited  $400;  April 
25,  deposited  $36;  May  10,  deposited  $10;  June   15,  withdrew 
$140.    What  was  the  balance  to  his  credit  July  1,  1905,  interest  4% 
quarterly  ? 

NOTE. — Arrange  in  the  form  of  an  account  and  extend  the  balances 
as  in  the  previous  problem. 

7.  A  opened  an  account  with  a  savings  bank  and  deposited 
July  1,  1905,  $200,  withdrew  July  20,  $40;  deposited  August  8, 
$230;  deposited  August  20,  $78;  withdrew  September  5,  $100; 
deposited   September  28,  $185;   deposited  October   14,  $137.50; 
withdrew  October  27,  $30;  deposited   November  13,  $150;   de- 
posited  November,  18,  $75 ;  withdrew   December   5,   $60 ;  with- 
drew December  13,  $45.    What  was  due  him  January  1,  1906,  in- 
terest being  ±%  payable  quarterly? 

19 


290  NEW   BUSINESS   ARITHMETIC 

S.  A  deposit  account  upon  the  ledger  of  a  savings  bank 
stood  as  follows:  July  1,  1905,  balance  $198.98;  July  1,  1905,  in- 
terest, $1.80;  July  15,  withdrawal,  $75;  September  10,  deposits 
$3000 ;  September  28,  withdrawal,  $125 ;  October  3,  withdrawal, 
$485 ;  October  19,  withdrawal,  $500 ;  December  9,  deposit  $162.32  ; 
December  14,  withdrawal,  $200;  December  31,  withdrawal,  $25. 
What  will  be  due  the  depositor  January  1,  1906,  interest  quarterly 
at  4%  ? 

9.  The  balance  due  a  depositor  at  a  savings  bank  January  1, 
1905,  was  $450;  February  3  he  deposited  $300;  February  15, 
withdrew  $85;  March  16,  deposited  $627.50;  March  24,  with- 
drew $250;  April  5,  deposited,  $1000;  April  18,  withdrew  $48.60; 
May  14,  deposited  $186.30 ;  May  16,  withdrew  $45 ;  June  4,  de- 
posited $75.30;  June  12,  withdrew  $280;  June  13,  withdrew  $43; 
July  17,  deposited  $78.40;  July  24,  withdrew  $126.80;  August 
4,  deposited  $15 ;  August  11,  deposited  $125 ;  September  25,  with- 
drew $250 ;  September  30,  withdrew  $175 ;  October  5,  deposited 
$80 ;  October  18,  deposited  $145 ;  October  27,  deposited  $437.25 ; 
November  15,  withdrew  $160;  December  11,  withdrew  $500; 
December  18,  deposited  $25 ;  December  24,  withdrew  $850.  What 
was  the  amount  of  his  credit  on  January  1,  1906,  interest  at  4%, 
payable  semi-ami ually  ? 

10.  What  would  be  due  a  depositor  at  the  end  of  the  year, 
who  had  a  balance  of  $1843  in  bank  on  January  1,  1905  ;  January 
8,  deposited  $145.60;  January  25,  deposited  $427.30;  February  15, 
withdrew  $180 ;  February  26,  withdrew  $286 ;  March  7,  deposited 
$85 ;  March  23,  withdrew  $1240 ;  May  16,  deposited  $275 ;  May 
23,  withdrew  $143;  June  12,  deposited  $1438;  June  18,  with- 
drew $745 ;  July  7,  withdrew  $100 ;  July  26,  withdrew  $40 ;  July 
29,  deposited  $200;  August  14,  withdrew  $1350;  August  25,  de- 
posited $180 ;  September  14,  deposited  $460 ;  September  28,  with- 
drew $245;  October  9,  deposited  $180;  October  23,  withdrew 
$500;  October  27,  deposited  $1500;  November  5,  withdrew  $640; 
November  17,  deposited  $340;  November  20,  deposited  $60;  De- 
cember 18,  deposited  $250;  December  31,  withdrew  $47.50.  The 


BANKS    AND    BANKING  291 

bank  allows  interest  at  4%  from  the  first  of  each  month  on  all  de- 
posits remaining  in  during  an  entire  month,  credited  quarterly. 

NOTE. — Take  the  smallest  balance  in  each  month  of  the  first  quarter, 
add  them  together,  and  (Jivide  by  three  to  get  the  average  balance  on 
which  interest  will  be  allowed.  Take  1%  of  this.  The  result  is  the  interest 
allowed  for  the  quarter.  Do  the  same  for  each  quarter. 

11.  A's  account  stands  credited  January  1,  1905,  $435:  Janu- 
uary  15,  deposited  $250;  February  1,  withdrew  $145;  March  10, 
withdrew  $84 ;  April  17,  deposited  $75 ;  April  25,  withdrew  $300 ; 
May  22,  deposited  $250 ;  June  18,  deposited  $60 ;  July  28,  deposited 
$340 ;  July  31,  withdrew  $800  ;  August  14,  deposited  $60  ;  Septem- 
ber 27,  withdrew  $25 ;  October  20,  deposited  $38.50;  November  5, 
withdrew  $150;  December  14,  deposited  $230.  What  will  be  the 
balance  January  1,  1906,  interest  allowed  at  4%  on  average 
monthly  balances,  and  credited  up  semi-annually  ? 

NOTE. — Take  the  smallest  balance  in  each  month  of  the  first  half  year, 
add  them  together,  and  divide  by  six  to  get  the  average  balance  on  which 
interest  will  be  allowed.  Take  2%  of  this.  The  result  is  the  interest 
allowed  for  the  half  year.  Do  the  same  for  the  second  half  year. 

'12.  A  clerk  had  on  deposit  in  a  savings  bank  July  1,  1905,  a 
balance  of  $625;  July  20,  deposited  $40;  August  3,  withdrew 
$130;  August  17,  deposited  $65;  September  24,  withdrew  $28.50; 
October  5,  withdrew  $90 ;  October  27,  deposited  $54.80 ;  Novem- 
ber 11,  deposited  $43;  November  18,  deposited  $40;  November 
30,  withdrew  $160;  December  12,  deposited  $48.50 ;  December  17, 
withdrew  $24.60.  What  will  be  his  balance  January  1,  1906.  in- 
terest allowed  at  4%  on  average  monthly  balances  and  credited 
up  quarterly? 

13.  What  will  be  the  amount  of  John  C.  Duncan's  balance  at 
the  end  of  the  year,  in  a  savings  bank  which  allows  4%  interest  on 
average  monthly  balances,  and  credits  up  the  interest  at  the  end 
of  each  quarter,  his  account  standing  as  follows :  January  1, 
1905,  balance  brought  down  $435;  January  17,  deposited  $86; 
February  20,  withdrew  $135;  March  13,  withdrew  $136.25; 
March  26,  deposited  $800;  April  16,  withdrew  $475;  May  10, 
withdrew  $500;  June  4,  deposited  $36.80;  June  28,  withdrew 
$75;  July  11,  deposited  $600;  August  14,  withdrew  $586;  Sep- 
tember 18,  deposited  $267;  October  15,  withdrew  $56;  Novem- 
ber 15,  deposited  $180;  December  4,  withdrew  $250;  December 
26,  withdrew  $65. 


TAXES 

426.  A  Tax  is  a  sum  assessed  on  persons  or  property  to  pay 
the  expenses  of  a  State,  County  or  City  or  for  other  public  pur- 
poses. 

427.  Taxes  levied  by  the  General  Government  are  of  two 
kinds:    Duties  or  Customs  and  Internal  Rei'cnue. 

428.  Taxes  levied  by  the  State,  County  or  City  are  of  two 
kinds  :    Property  and  Poll  Tax. 

429.  Property  Tax  is  a  Tax  on  property  reckoned  at  a  cer- 
tain per  cent,  on  the  assessed  value. 

430.  Poll  Tax  is  a  tax  assessed  on  persons ;  in  most  of  the 
states  on  all  male  citizens  over  21  years  of  age. 

431.  An  Assessor  is  a  person  elected  to  estimate  the  valua- 
tion of  taxable  property. 

432.  A  Collector  is  an  officer  whose  duty  it  is  to  receive  and 
collect  taxes. 

In  some  states  collectors  are  paid  a  certain  per  cent,  for  their  services, 
and  the  amount  levied  must  include  the  amount  of  money  necessary  to 
be  raised  plus  the  collector's  fee. 

In  computations  in  taxes, 

1.  Assessed  Valuation  =  Base.     2.  Ta.r=  Percentage. 

ORAL  PROBLEMS 

1.  What  is  A's  tax  on  property  assessed  at  $4800,  the  tax  levy 
.being  \\%  ?  \\%  ?  \%  ?  \%  ? 

2.  What  is  a  person's  tax  whose  property  is  assessed  at  $5000, 
when  the  rate  of  taxation  is  2$%  ?  \\%  ?  \\%  ? 

3.  A's  property  is  valued  at  $6000,  the  assessed  valuation  is 
f .    What  is  the  tax,  the  rate  of  taxation  being  \\%  ?  lj-%  ?'  \\%  ? 

4.  What  is  a  person's  tax  on  property  valued  at  $10000  as- 
sessed at  f  valuation  when  the  rate  of  taxation  is  1%  and  who 
also  pays  poll  tax  for  4  persons  at  $1.50  each? 

5.  A  tax  of  $36  is  paid  on  property  assessed  at  a  rate  of  \%. 
What  is  the  assessed  valuation  ? 

292 


TAXES  293 

ti.  A  tax  of  $50  is  paid  on  property  assessed  at  \%.  What  is 
the  value  of  the  property,  the  assessed  valuation  being  at  J  valua- 
tion? 

WRITTEN   PROBLEMS 

1.  A  paid  tax  on  $49200  at  the  rate  of  $.008^  on  the  dollar, 
and  paid  2  polls  at  $1.75  each.    What  amount  of  tax  did  he  pay? 

2.  How  much  must  I  pay  on  property  worth  $9840,  assessed 
for  f  its  value  at  $.011f  on  the  dollar,  and  three  polls  at  $2.10 
each  ? 

3.  A  village  containing  220  taxable  persons  whose  property 
was  valued  at  $418500,  was  assessed  for  the  purpose  of  building 
a  school  house,  at  $.013  on  the  dollar  and  $1.80  each  for  polls. 
What  was  the  cost  of  the  school  house? 

4.  A  tax  of  $.010£  on  the  dollar  and  $1.35  for  polls  was  as- 
sessed in  Warren  county  for  the  purpose  of  building    a    court 
house.     The  value  of  property  was  $987430,  and  the  number   of 
taxable  persons  1342.    Allowing  2$%  for  collecting,  what  amount 
was  paid  for  the  court  house  ? 

o.  What  amount  of  tax  is  paid  on  $43500  worth  of  property 
assessed  for  f  its  value  at  $.01 2 J  on  the  dollar,  and  34  polls  at 
$1.20  each? 

G.  For  the  purpose  of  paving  a  street  the  property  owners  on 
the  street  were  assessed  on  $214700  worth  of  property  at  $.009  j 
on  the  dollar,  and  $.85  each  on  94  polls.  The  charges  for  collect- 
ing were  4-J%.  What  did  the  pavement  cost? 

7.  A  town  assesses  a  tax  of  $.012£  on  the  dollar,  and  $1.18 
each  on  115  polls.     The  personal  property  worth  $86280  is  as- 
sessed for  |  its  value,  and  real  estate  $65296  for    J    its    value. 
What  was  the  amount  of  tax  ? 

In  practical  tax  computations  a  Tax  Table  is  prepared  by  the 
use  of  which  the  labor  of  finding  the  tax  is  greatly  reduced. 

8.  The  assessed  value  of  the  property  in  a  school  district  is- 
$220488,  and  a  tax  of  $1625  is  voted.     Construct  a  tax  table 
similar  to  the  one  on  the  following  page. 


294 


NEW   BUSINESS   ARITHMETIC 


TAX    TABLE — 7.37    MILLS    ON    $1 


0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

1 

.07370 

.08107 

.08844 

.09581 

.10318 

.11055 

.11792 

.12529 

.13266 

.  14003 

2 

.14740 

.15477 

.16214 

.16951 

.17688 

.  18425 

.19162 

.19899 

.20636 

.21373 

3 

.22110 

.22847 

.23584 

.24321 

.25058 

.25795 

.26532 

.27269 

.28006 

.28743 

4 

.29480 

.30217 

.30954 

.31691 

.32428 

.33165 

.33902 

.34639 

.35376 

.36113 

5 

.36850 

.37587 

.38324 

.39061 

.39798 

.40535 

.41272 

.42009 

.42746 

.43483 

6 

.44220 

.44957 

.45694 

.46431 

.47168 

.47905 

.48642 

.49379 

.50116 

.50853 

7 

.51590 

.52327 

.53064 

.53801 

.54538 

.55275 

.56012 

.56749 

.57486 

.58223 

8 

.58960 

.59697 

.60434 

.61171 

.61908 

.62645 

.63382 

.64119 

.64856 

.65593 

9 

.66330 

.67067 

.67804 

68541 

.69278 

.70015 

.70752 

.71489 

.72226 

.72963 

SOLUTION 

Tax  on  $1300  = 
Tax  on         80  = 


>.581 
.589 


Tax  on  $1380  =  $10.1' 


From  the  table  find  the  tax  on  A's  property  which  is  assessed 

$1380. 

EXPLANATION. — Look  in  the  table  op- 
posite 1  in  the  left  hand  column  and 
under  3  in  fifth  column  and  we  find  the 
tax  on  $13  is  .09581.  Removing  the 
decimal  point  two  places  to  the  right 
which  is  equivalent  to  multiplying  by 
100  and  we  have  the  tax  on  $1300  =  to 
$9.581.  Then  looking  opposite  8  and  under  0  and  we  find  the  tax  on  $80 
to  be  .589.  Adding  these  together  we  have  the  total  tax. 

P.  According  to  the  table  what  will  be  the  amount  of  A.  C. 
Bore's  tax  if  his  property  is  assessed  $24365'  and  he  pays  for  3 
polls  at  $1.80  each? 

10.  After  May  1  a  penalty  of  \%  per  month  is  added  to  all 
unpaid  taxes.     S.  D.  Johnson's  property  is  assessed  at  $42630 
and  he  pays  for  2  polls  at  $1.50  each.    If  he  pays  his  tax  August 
3,  what  amount  must  he  pay  ? 

11.  The  amount  of  money  to  be  raised  by  taxes  in  Ottawa  is 
$212093.20.     The  taxable  property  is  $11522400,  and  there  are 
3350   polls,    each   at   $1.40.     Find  the  rate  of  taxation.     If  the 
assessment  is  made  on  a  J  valuation,  what  would  be  the  rate? 


CUSTOMS   OR  DUTIES 

433.  Customs  or  Duties  are  taxes  levied  on  imported  goods 
for  the  support  of  the  general  government,  and  the  protection  of 
home  industries. 

434.  Ad  Valorem  Duty  is  a  tax  of  a  certain  per  cent,  on  the 
cost  of  the  goods  in  the  country  from  which  they  were  imported. 

435.  Specific  Duty  is  a  tax  levied  on  goods  without  regard 
to  value  but  estimated  on  weight  or  measure. 

In  some  cases  duties  are  ad  valorem;  on  some  articles  they  are  specific; 
and  some  others  they  are  both  ad  valorem  and  specific. 

436.  An  Invoice  on  imported  goods  is  an  itemized    list    of 
goods  shipped  and  their  value  in  the  country  of  origin. 

All  invoices  on  imported  merchandise  must  be  made  out  in  the 
currency  of  the  country  of  export  and  must  be  certified  by  the 
United  States  consul,  vice  consul  or  commercial  agent  in  the 
country  from  which  the  goods  are  exported. 

437.  Consul  Fee  is  a  charge  made  by  the  consul  but  it  is  not 
a  part  of  the  dutiable  value. 

438.  Tare  is  an  allowance  made  for  the  weight  of  a  box,  bag, 
etc.,  containing  the  goods. 

439.  Leakage  is  an  allowance  made  for  waste  of  liquors  in 
barrels. 

440.  Breakage  is  not  allowed  for  loss  of  liquors  in  bottles, 
but  shortage  occurring  before  shipment  will  be  considered. 

441.  Gross  Weight  is  the  weight  before  any  deductions  are 
made.  . 

442.  Net  Weight  is  the  weight  after  the  deductions  are  made. 

443.  A  Tariff  is  a  list  of  goods,  giving  the  rate  of  duty  pre- 
scribed by  law. 

444.  A  Custom  House  is  a  government  building  or  office 
where  duties  are  assessed  and  collected  and  all  other  government 
business  concerning  that  port  is  transacted. 

295 


296  NEW   BUSINESS   ARITHMETIC 

Goods  cannot  be  legally  imported  except  through  the  custom 
house  at  a  regular  port  of  entry. 

445.  A  Port  of  Entry  is  a  town  or  city  in  which  a  custom 
house  is  located. 

The  chief  port  of  entry  in  the  United  States  is  New  York,  but 
all  of  the  principal  cities  are  ports  of  entry. 

446.  Smuggling  is  secretly  bringing  goods  into  a  country  to 
avoid  the  payment  of  duties. 

Smuggled  goods  when  found  are  subject  to  seizure  and  the 
person  or  persons  found  guilty  of  such  violations  of  the  law, 
liable  to  a  fine  or  imprisonment  or  both. 

447.  A  Bonded  Warehouse  is  a  building  used  for  the  storage 
of  imported  merchandise  until  the  duties  shall  have  been  paid. 

Goods  held  for  duties  are  said  to  be  "in  bond"  and  10%  extra  dun- 
is  charged  for  each  year  that  they  remain  in  bond.  If  left  for  more  than 
three  years  they  are  considered  as  abandoned  to  the  government,  and  are 
advertised  and  sold  at  auction  for  payment  of  the  duties. 

448.  Internal  Revenue  is  the  taxes  levied  on  goods  manufac- 
tured and  sold  in  this  country  for  the  purpose  of  government  sup- 
port. 

Internal  revenue  taxes  are  usually  paid  by  affixing  government  stamps 
to  the  package  containing  the  articles  to  be  taxed,  or  by  purchasing  a 
government  license. 

In  estimating  ad  valorem  duties, 

1.  Cost  =  Base.          2.  Duty  =  Percentage. 

NOTES. — 1.  In  estimating  ad  valorem  duties  all  charges  necessary  to 
prepare  goods  for  shipment  must  be  added  to  net  cost  of  goods  to  find  the 
dutiable  value. 

2.  In  finding  specific  duties  the  long  ton   (2240  Ibs.)   is  used.  Allow- 
ances— Tare,  Leakage,  etc.,  are  deducted  before  the  duty  is  estimated. 

1.  What  is  the  amount  of  duty  on  a  shipment  of  2500  Ibs. 
invoiced  at  3  shillings  per  pound*,  the  rate  of  duty  being  7c  per 
pound  and  5%  ad  valorem,  4%  being  allowed  for  tare? 

NOTE. — One  shilling  =  24^  cents. 

2.  L.  M.  Hawthorne  received  from  London  one  case  of  mer- 
chandise, weighing  570  Ibs.  net.     The  invoice    price    was    £370 
10s;  packing  charges  £10  8s.     The  ad  valorem  duty  was  28%; 
the  specific  duty  12$  cents  per  Ib.    What  was  the  entire  duty? 


CUSTOMS    OR    DUTIES  297 

NOTE. — Add   all   charges   to   net   cost   to   find   dutiable   value.     £1   = 

$4.8665. 

3.  A  manufacturer  imported  from  England  35  bales  of  wool, 
weighing  440  Ibs.  each;  tare  5%;  cost  2^s.  per  Ib. ;  specific  duty 
6  cents  per  Ib.    What  was  the  duty  ? 

NOTE. — The  tare  is  deducted  before  finding  cost  and  specific  duty. 

4.  R.   G.  Waltz  &  Co.  received  an  invoice  of  goods  from 
France,  amounting  to  4250  francs  on  which  there  was  8%    dis- 
count.    The  charges  subject  to  duty  were  213.9  francs.     What 
was  the  duty  at  40%  ? 

NOTE.— 1  franc  =  19.3c. 

5.  H.  J.  Graham  imported  from  Paris  one  case  silk  shawls. 
The  first  cost  was  8340  francs ;  packing  charges  215.05  francs ; 
the  net  weight  842.    \Vhat  was  the  entire  cost,  at  60%  ad  valorem 
duty  ? 

6.  John  W.  Hauser  &  Co.  received  from  Berlin  an  invoice  of 
books  amounting  to  3284  marks.     Case  and  packing  cost  243.84 
marks.    What  was  the  duty  at  25%  ? 

NOTE.— 1  mark  =  23.8c. 

7.  A  merchant  imported  from  Germany  a  box  of  merchandise 
invoiced  at  2365  marks,  on  which  there  was  a  discount  of  8%  ; 
charges  173.95  marks.     Net  weight  was  920  Ibs.     What  was  the 
duty  at  9  cents  per  Ib.  and  25%  ad  valorem? 

S.  An  invoice  of  merchandise  amounting  to  3148  guilders  was 
received  at  the  Chicago  Custom  House.  The  charges  for  case 
and  packing  were  230.05  guilders.  What  was  the  duty  at  36%  ; 
the  par  value  of  a  guilder  being  40.2  cents? 

0.  A  merchant  received  from  Brussels  1972  yds.  of  carpet 
24  inches  wide  invoiced  at  6  francs  per  yd.  on  which  4.%  discount 
was  allowed.  The  charges  were  394.77  francs.  What  was  the 
entire  cost  with  specific  duty  44  cents  per  square  yard  and  ad 
valorem  duty  40%? 

10.  A  hardware  merchant  imported  from  England  one  box  of 
50  doz.  assorted  knives  invoiced  at  £270  6s.  9d.,  on  which  he  was 
allowed  a  discount  of  5  and  5%.  The  charges  were  £16  18s.  4.8d. ; 


298 


NEW   BUSINESS   ARITHMETIC 


net  weight  740  Ibs.     What  was  the  entire  cost  at  20  cents  each, 
specific  duty  and  40%  ad  valorem? 

11.  A  dry  goods  merchant  imported  from  Manchester,  Eng- 
land, 7  cases  white  muslins  containing  1440  pieces,  each  piece 
being  27  yards  long  and  1J  yards  wide,  the  muslin  was  invoiced 
at  3Jd.  per  yard,  and  the  total  charges  were  £32  17s.  6d.    What 
was  the  duty  on  the  invoice  at  4|  cents  per  square  yard  and  20% 
ad  valorem? 

12.  Invoice  received  by  F.  K.  RACHLER  £  Co.,  St.  Louis,  Mo. 


Marks 

Nos. 

Packages  and  Contents 

Cost 

F.  K.  R. 

61 
62 

1  Case  Carpet  1120  yds..  18  in.  wide, 
@  4  francs    *** 
1  Case  Carpet  780  yds.,  24  in.  wide, 
@  3^  francs    *** 

Case  and  Packing 

Total  cost 
Specific  duty  22c  pr.  sq.  yd. 
Ad  Valorem  duty  40$  on  $ 

Entire  Cost 

**** 
174.6 

#**# 
##*  ** 

####  #* 

NOTE. — Find  total  cost  in  francs  and  reduce  to  U.  S.  money. 

13.  Invoice  of  one  case  of  good,s  from  B.  A.  WELSTEAD  & 
Co.,  Liverpool,  England,  for  R.  T.  RILEY  &  Co.,  Louisville,  Ky. 


Marks 

Nos. 

Packages  and  Contents 

Duty 

Ad. 

Spec. 

R.  T.  R. 

428 

720  vds.  Velvet,  22  in.  wide,  @  £1  12s.  yd. 
I960  "     Chiffon  Lace  @  2s.  4d.  yd. 
1120  "     Carpet,  18  in.  wide,  (cb  15s.  yd. 
2180  "    Carpet,  26  in.  wide,  @  10s.  6d.  yd. 

Net  Cost 
Duty  on  Velvet 
"       "    Lace 
"    Carpet 
"       "    Carpet 

Total  Cost 

25# 

60;? 

40$ 
60^ 

18c  pr.  sq.yd. 

60cpr.  sq.yd. 
60c  pr.  sq.yd. 

>••.>;-.;;:*>;-.    ## 

EQUATION   OF   ACCOUNTS 

449.  An  Account  is  a  record  of  business  transactions  and 
may  embrace  either  debits  or  credits  or  both. 

450.  Equation  of  Accounts  is  the  process  of  finding  the  time 
when  several  debts  due  at  different  times,  may  be  paid  at  one  time 
without  loss  to  either  party,  or  if  the  account  has  two  sides,  when 
the  balance  or  difference  may  be  paid. 

451.  Cash  Balance  is  the  sum  required  to  pay  an  account  at 
-any  given  date. 

453.  The  Term  of  Credit  is  the  time  a  debt  has  to  run,  as  10 
days,  1  month,  90  days,  etc. 

All  accounts  bear  legal  interest  after  they  become  due. 

Promissory  notes,  not  containing  an  interest  clause,  bear  legal 
interest  -after  maturity. 

453.  The  Average  Term  of  Credit  is  the  average  of  the  sev- 
ceral  terms  <of  credit. 

454.  The  Equated  Time  is  the  date  at  which  the  payment  of 
two  or  more  debts  may  be  made  in  one  payment  without  loss  to 
icit'her  debtor  or  creditor. 

455.  The  Focal  Date  is  any  assumed  date  of  settlement  from 
•which  we  reckon. 

By  assuming  any  date  as  a  focal  date,  we  find  what  the  gain 
or  loss  of  interest  would  be  to  the  payer,  if  all  the  debts  were  paid 
"by  "him  on  that  date. 

We  then  find  the  time  the  whole  amount  would  produce  this 
interest,  and  add  the  time  thus  found  to,  or  subtract  it  from,  the 
focal  date  to  find  the  true  date  of  settlement. 

456.  To  find  the  equated  time  when  the  account  consists  of 
'Only  debits  or  credits. 

1.  On  January  1,  1905,  I  sold  to  P.  J.  Weaver,  a  house  pay- 
able as  follows :     $200  in  3  months ;  $400  in  5  months ;  $500  in 

299 


300  NEW    BUSINESS    ARITHMETIC 

12  months;  $100  in  16  months.  What  is  the  average  term  of 
credit  and  the  date  when  the  whole  amount  should  be  paid  ? 

SOLUTION PRODUCT  METHOD  EXPLANATION.— 

Assume  Jan.  1,  1905,  as  the  date  of  settlement.  If  Weaver  should 

$200   X     3             =       $600.  Pav    the    $200    on 

$400    X      5              =     $2000.  Jan-   !»   1905>  he  would  pay  it 

$500    X    12              =     $6000.  3  mo-  before  il:  is  due,  and  the 

$100    X    16               =     $1600.  interest   on  $200   for  3  mo.    = 

—  the  interest  on  $600  for  1   mo 

$1200  (due  me)              $10200.  chle  Weaver     The  interest  on 

$10200  -r-  $1200         =  8J  mo.      $400  for  5  mo    =  the  interest 
Jan.  1  +  8|  mo.  =  Sept.  16.  on  $2000  for  1  mo.  due  Weaver, 

The  interest  on  $500  for  12  mo. 

equals  the  interest  on  $6000  for  1  mo.  due  Weaver.  The  interest  on  $100 
for  16  mo.  equals  the  interest  on  $1600  for  1  mo.  due  Weaver.  Adding  we 
find  that  Weaver  owes  me  $1200  but  I  owe  him  the  interest  upon  (or  use 
of)  $10200  for  1  mo.  Now  the  interest  on  $10200  for  1  mo.  is  equal  to  the 
interest  on  $1200  for  Sl/2  mo.  Therefore  Weaver  may  withhold  the  $1200 
due  me  Sl/2  months  or  until  September  16. 

SOLUTION INTEREST  METHOD 

Assume  Jan.  1,  1905  as  the  date  of  settlement. 
Int.  on  $200  for     3  mo.  at  6%  =    $3.        EXPLANATION.-!!  Weaver 
Int.  on  $400  for    5  mo.  at  6%  =  $10.    had  Paid  the  several  sums 
Int.  on  $500  for  12  mo.  at  6%  =  $30.    on  January  1,  1905,  I  would 
Int.  on  $100  for  16  mo.  at  6%  =    $8.    have  owed  him  $51  interest, 

-    hence  he  may  keep  the  $1200 

$1200  (due  me)  $51.     principal    until    the    interest 

Int.  on  $1200  for  1  mo.  at  6  %  =  $6.      On  it  amounts  to  $51.    Any 

$51  -i-  $6  =  8^  mo.  rate  of  interest  may  be  used, 

Jan.  1  +  8i  mo.  ==  Sept.  16.  but  it  is  most  convenient  to 

use  6%. 

NOTES. — 1.  In  finding  the  average  term,  fractions  of  a  day  of  one-half 
or  more  are  counted  as  one  day;  fractions  less  than  one-half  are  rejected. 
2.  The  product  method  is  recommended  because  it  involves  less  work 
and  is  more  easily  comprehended  by  the  student,  but  accountants  prefer  the 
interest  method.  Both  methods  should  be  used  until  thoroughly  under- 
stood. 

2.  On  March  5,  1905,  B  bought  the  following  bill  from  A : 
$240  on  10  days  time,  $300  on  20  days  time,  $450  on  30  days 
time,  $600  on  60  days  time.  Find  the  date  when  the  whole  sum 
can  be  paid  without  loss  to  either  party. 


EQUATION    OF    ACCOUNTS  301 

3.  Jones  bought  a  lot  of  merchandise  for  $2100  from  Brown 
of  which  $400  was  payable  in  2  months ;  $500,  in  3.  months ;  $300, 
in  G  months ;  $200,  in  8  months ;  $700,  in  9  months.     What  is  the 
average  time  of  credit  of  the  whole  amount? 

4.  I  owe  $150  due  in  4  months;  $300  due  in  6  months;  $600 
due  in  1)  months;  $800  due  in  12  months.     What  is  the  average 
time  of  credit? 

5.  Lyman  bought  a  house  on  April  16,  1903,  for  $2000,  pay- 
able as  follows;  J  cash,  -J  in  5  months,  f  in  8  months,  the  re- 
mainder in  10  months.     What  is  the  equated  time  for  paying  the 
whole,  and  the  maturity  of  a  note  for  the  entire  amount  ? 

6.  Graham  sold  the  following^  merchandise  on  June  3,  1905 : 
$200  worth  of  prints  on  30  days ;  $360  worth  of  flannels  on  2 
months ;  $420  worth  of  silks  on  60  days ;  $560  worth  of  cotton 
goods  on  90  days.     When  can  the  whole  amount  be  paid  by  the 
debtor  without  loss  of  interest  ? 

7.  A  bought  a  farm  on  January  10,  1905,  for  $7200,  of  which 
$1200   was   paid   in   cash,   $1000   was  to  be  paid   in   3   months; 
$1200,  in  6  months;  $1400,  in  9  months;  $1300,  in  12  months; 
the  remainder,  in  15  months.     He  gave  his  note  for  the  amount 
due  after  making  the  cash  payment.     What  should  be  the  ma- 
turity of  the  note  ? 

(9.  I  bought  the  following  goods  from  Fuller  &  Co.  on  July  1, 
1905:  $180  on  10  days;  $210  on  30  days;  $340  on  60  days; 
$620  on  90  days;  $750  on  4  months;  $200  on  6  months.  Find 
the  maturity  of  my  note  given,  to  pay  the  entire  amount. 

9.  Find  the  equated  time  and  date  of  settlement  of  the  fol- 
lowing, sold  on  May  21,  1905:  $160  on  15  days;  $360  on  1 
month;  $190  on  40  days;  $425  on  2  months;  $230  on  90  days; 
$490  with  no  term  of  credit ;  $85  on  4  months ;  $310  on  5  months ; 
$660  on  5  days;  $900  on  10  days;  $515  on  20  days;  $740  on  25 
days. 

10.  March  20,  I  bought  a  horse  for  $175,  on  a  credit  of  4 
months;  May  5,  a  harness  for  $35,  on  3  months;  and  June  15,  a 
carriage  for  $225,  on  6  months.  Find  the  equated  time  for  the 
payment  of  these  debts. 


302 


NEW    BUSINESS    ARITHMETIC 


SOLUTION 


July  20 

$175 

.... 

Aug.  5 

35 

16 

560 

Dec.  15 

225 

148 

33300 

$435 

$33860 

March  20  +  4  mo. 
May  5  +3  mo. 
June  15  +6  mo. 


$33860  -i-  $435  =  78  =  78  da.  average  term  of  credit. 
July  20  +  78  da.  =  Oct.  6,  equated  time. 

Find  the  equated  time  for  the  settlement  of  the  following  bills : 


11.     Bill  No.  1.  Terms  cash. 

1905 

Feb.  2,      .       Mdse.    $425. 
March  10,  $320. 

May  6,  $195. 

June  30,  "      $1120. 


12.    Bill  No. 

2.    Terms  30  days 

1905 

June  2, 

Mdse.  $247.20. 

July  14, 

$165. 

July  30, 

"      $280. 

August  4, 

"      $760. 

William  Hammond, 


IS.     Bill  No.  3 


To  P.  D .  Armour  &  Co.  Dr. 


1905 

Apr. 

2 

40 

bbl.  Beef 

30  da. 

$18.50 

May 

14 

60 

Mess 

Pork 

60  da. 

$10.25 

June 

8 

25 

"    Short 

Ribs 

90  da. 

$  2.75 

14.     Bill  No.  4. 
1905 
Oct.  22,   Mdse.  1  mo.,  $116.20. 


Dec.  14, 

1906 
Jan.  18, 
March  11, 
May  4, 


2  mo.,  $275. 

3  mo.,  $79.25. 

1  mo.,  $367.40. 

2  mo.,  $67.85. 


15.     Bill  No.  5. 
1905 
April  6,  Mdse.  10  da.,  $236.10. 


May  2, 
May  23, 
June  7, 
July  2, 


20  da.,  $71.15. 
15  da.,  $329. 
30  da.,  $143.50. 
60  da.,  $420. 


EQUATION    OF    ACCOUNTS 


303 


16.  Bill  No.   6. 
1905 

Feb.  4,      Mdse.  30  da.,  $72,45. 

March  12,  "      10  da.,  $16.90. 

April  23,  "      (cash)   $41.20. 

May  1,  "      20  da.,  $62. 
June  6,  15  da.,  $98.10. 

July  12,  "      30  da.,  $26.35. 


17. 

1904 
Oct.  30, 

1905 

April  27, 
August  1, 

1906 
Jan.  21, 
May  1, 


Bill  No.  7. 
Mdse.   6  mo.,  $250. 

"      10  da.,  $365. 
3  mo.,  $270. 

"      60  da.,  $124. 

"      30  da.,  $417. 


18.  Find  the  equated  time  for  settlement  of  the  following": 

STATEMENT    OF    ACCOUNT 

Boston,  Sept.  1,  1905. 
Charles  D.  Rogers, 

In  account  with  French,  Potter  &  Wilson. 


1905 

January 

10 

To  Mdse.                                                   SO  da. 

162 

SO 

April 

19 

60  da. 

321 

45 

June 

24 

Cash 

99 

August 

10 

4  mo. 

172 

754 

75 

457.   To  find  the  equated  time  for  the  payment  of  the  balance 
of  an  account  having  both  debits  and  credits. 

1.  Find  the  equated  time  for  the  payment  of  the  balance  of 
the  following  account. 

Dr.  A.  R.  Harmon.  Cr. 


1905 

1905 

January 

1 

Mdse. 

400 

March 

4 

Cash 

200 

Feb. 

G 

« 

720 

(  t 

25 

<( 

350 

April 

2 

<( 

500 

When  an  account  has  both  debit  and  credit  sides  as  the  above, 
the  equated  time  for  the  payment  of  the  balance  may  be  found  by 
either  the  Product  Method  or  the  Interest  Method.  The  above 
problem  is  solved  by  both  of  these  methods  in  order  that  the  stu- 


304 


NEW   BUSINESS   ARITHMETIC 


dent  may   familiarize  himself  with  them.     Accountants   usually 
prefer  the  interest  method,  as  it  appears  more  business-like. 

SOLUTION PRODUCT    METHOD 

FOCAL    DATE,    JANUARY    1,    1905 


ITEMS.        TIMES.          PRODUCT. 


Jan.  1,  $400  '  0 
Feb.  6,  $720  36 
Apr.  2,  $500  91 

$1620 
550 


000 

$25920 
$45500 


ITEMS.      TIMES.       PRODUCT. 


March  4,  $200   62   $12400 
March  25,  $350   83   $29050 


$550 


$41450 


$71420 
41450  Subtracting  smaller  side. 


$1070  $29970 

$29970  -^-  $1070  =  28  da.  =  average  term  of  credit. 
Jan.  1,  1905  -f  28  da.  =  Jan.  29,  1905,  equated  time  of  pay- 
ment. 

EXPLANATION. — Assuming  Jan.  1,  1905,  as  the  focal  date  we  find  the 
products  upon  the  Dr.  and  Cr.  sides  as  in  previous  problems.  Then  sub- 
tracting the  credit  from  the  debit  side  we  find  the  balance  of  the  items 
to  be  $1070  and  the  balance  of  the  products  to  be  $29970  both  in  favor  of 
the  debit  side.  Therefore  the  balance  of  the  account  $1070  is  entitled  to  a 
credit  long  enough  to  equal  $29970  for  one  day,  which  we  find  by  dividing 
to  be  28  days.  This  added  to  the  focal  date  gives  Jan.  29,  1905. 

Should  the  balance  of  the  items  be  on  one  side  and  the  balance 
of  the  products  on  the  other  side  of  the  account,  if  the  earliest 
date  is  taken  as  a  focal  date,  the  balance  of  the  account  must  suffer 
a  discount,  or  be  due  prior  to  the  focal  date,  and  hence  we  count 
back  of  the  focal  date  to  find  the  equated  time. 

SOLUTION — INTEREST    METHOD 


APRIL    2, 

INTEREST. 

$6.07 
$6.60 
0 

1905.      INTEREST    6#. 

DUE.                    ITEMS.              TIMES.    IN 

Mar.  4,       $200     29  da. 
Mar.  25,     $350       8  da. 

TEREST. 

.97 
.47 

$550 

Smaller  side  subtracted. 
Int.  on  $1070  for  1  da.  = 

$1.44 
$.17$. 

$12,67 
1.44 

$11.23 

EQUATION    OF    ACCOUNTS 


305 


$11.2-3  -T-  $.17ft  =  63  da.  average  term  of  credit. 
April  2 — 63  da.  =  Jan.  20,  equated  time  of  payment. 

NOTES. — 1.  Any  date  may  be  taken  as  a  focal  date,  but  it  simplifies  the 
reasoning  to  assume  either  the  earliest  or  the  latest  date,  the  result  being 
the  same  in  both  cas^s. 

2.  In  an  account  that  contains  both  debits  and  credits,  the  items  on  the 
debit  of  the  ledger  of  one  of  the  parties  are  the  same  as  those  on  the  credit 
of  the  ledger  of  the  other  party ;  hence,  an  account  equated  by  both  parties 
must  show  the  same  result. 

2.  Find  the  average  time  for  the  payment  of  the  balance  of 
the  following  account: 


Dr. 


A.  E.  BAKER. 


Cr. 


1905 

1905 

May 

12 

Mdse. 

370 

June 

4 

Cash 

220 

May 

31 

« 

192 

80 

July 

2 

" 

175 

80 

June 

14 

u 

126 

July 

26 

« 

150 

July 

6 

" 

217 

3.  When  is  the  balance  of  the  following  account  due? 
Dr.  ].  F.  SARLEY.  Cr. 


1905 

1905 

Jan. 
Feb. 

17 

27 

Mdse.,  30  days 
10    " 

300 
240 

Feb. 
Mch. 

1 
4 

Cash 
Note,  15  da. 

100 
150 

Mch. 
April 

12 

1 

"       20    " 
"       30    " 

450 
600 

April 
May 

6 
10 

Cash 

« 

350 
120 

NOTE. — Find  the  maturity  of  each  item  and  use  the  due  dates  in  equat- 
ing or  add  the  special  credit  to  time  from  regular  date. 

4.  Find  the  date  of  a  note  to  settle  the  balance  of  the  follow- 
ing accounts : 


Dr. 


F.  W.  C.  HOLTKAMP. 


Cr. 


1905 

1905 

A  lay 

1 
30 

Mdse.,    5  days 

15    " 

217 

192 

80 

June 

July 

4 
1 

Note,  20  da. 
Cash 

150 

68 

30 

June 

14 

30    " 

62 

30 

" 

15 

« 

209 

70 

'' 

27 

10     " 

377 

90 

20 


306  NEW   BUSINESS   ARITHMETIC 

5.  Average  the  following  account : 
Dr.  D.  C.  MEYER. 


Cr. 


1905 

1906 

Nov. 

20 

Mdse.,  3  months 

560 

Mch. 

5 

Draft,  15  da. 

250 

Dec. 

27 

"      3      " 

178 

April 

3 

Note,  1  mo. 

130 

1906 

Jan. 
Mch. 

31 
2 

"      60  days 
"      30    " 

93 

230 

45 
55 

May 

1 
15 

Cash 
Mdse.,  10  da. 

75 

180 

April 

17 

a 

120 

6. 

1 

When  is  the  balance  of  the  following  account  due? 

Dr.                               F.  D.  NEAGELE.                                 Cr. 

1905 

1905 

Jan. 

6 
30 

Mdse.,  30  days 

"       60     " 

272 
536 

15 

Mch. 
April 

2 

1 

Note,  20  da. 
Ck.  dated 

172 

Feb. 

20 

10    " 

73 

April  15 

300 

Mch. 

18 

15    " 

121 

60 

May 

24 

Cash 

150 

April 

12 

10    " 

83 

25 

31 

100 

7. 

Average  the  following  account  : 

Dr.                                  C.  W.   KITT.                                  Cr. 

1905 

1906 

Oct. 

1 

Mdse.,  2  months 

190 

Jan. 

1 

Cash 

130 

Dec. 

4 

30  days 

274 

Mch. 

19 

Acceptance 

1906 

Jan. 

11 

20    " 

311 

40 

(t 

24 

10  days 
Cash 

228 
173 

Feb. 
April 

21 

1 

20    " 

86 
217 

20 
95 

April 

1 

tt 

217 

95 

8.  What  is  the  balance  of  the  following  account,  and  when  will 
it  begin  to  draw  interest  ? 

Dr.  W.  J.  FISHER.  Cr. 


1905 

1905 

April 
May 

1 
4 

Cash 
Note,  10  days 

125 

200 

Jan. 
Feb. 

21 

28 

Mdse.,  60  da. 

90  " 

166 
219 

60 
28 

« 

1 

Sight  draft 

100 

April 

20 

"       20   " 

52 

80 

July 

1 

Cash 

250 

June 

30 

"       10   " 

356 

Aug. 

15 

u 

199 

63 

July 

14 

"       15   " 

411 

35 

30 

"       $380, 

4^  off 

*** 

** 

Aug. 

15 

"       $210, 

3  &  2fc  off 

*** 

** 

EQUATION    OF    ACCOUNTS 


307 


9.  When  must  a  note  be  dated  and  commence  drawing  inter- 
est if  given  in  settlement  of  the  following  account? 


Dr. 


W.  W.  COFFIN. 


Cr. 


1905 

1905 

July 

1 

Mdse.,  90  days 

208 

60 

Dec. 

1 

Cash 

360 

Oct. 

30 

$420, 

Art   nff 

*** 

** 

1906 

Feb. 

19 

Note,  30  da. 

135 

1906 
Jan. 
Mch. 

1 
3 

^/o  Ull 

20  days 

10    " 

114 
374 

50 
90 

April 
May 

1 
5 

Mdse.,  $220 
6^  off 
Cash 

*** 
123 

70 

May 

1 

"       $160 

5  &  5#  off 

*** 

** 

10.  Find  the  average  date  of  payment  in  the  following: 
Dr.  D.  C.  ROBERTS.  Cr. 


1903 

1904 

Aug. 

30 

Mdse.,  4  months 

210 

Jan. 

1 

Mdse.,  $120, 

Nov. 

3 

«      3       ,« 

147 

20 

3^  off 

**# 

**. 

1904 

May 

4 

"      60  days 

379 

35 

July 
Dec. 

1 
1 

Note,  3  mo. 
Cash 

230 
175 

Aug. 

6 

"      60    " 

430 

25 

1905 

*-*o 

Dec. 

12 

"      30    " 

53 

15 

Jan. 

30 

Mdse.,  30  da. 

291 

40 

19C5 

Jan. 

1 

"    $270, 

6  &  2#  off 

*** 

** 

11.  Find  the  balance  due  on  the  following  account,  July  10, 
1905,  interest  allowed  at  6%. 


Dr. 


L.  H.  YOUNG. 


Cr. 


1905 

1905 

Jan. 

4 

Mdse.,   10  days 

400 

Mch. 

21 

Cash 

200 

Feb. 

16 

20      " 

360 

April 

30 

Note,  15  da. 

150 

April 

5 

"       30      " 

500 

June 

3 

Cash 

120 

808 


NEW   BUSINESS   ARITHMETIC 


12.  If  the  following  account  is  settled  January  1,  1907,  money 
being  worth  7%,  what  amount  must  be  paid? 


Dr. 


B.  E.  IRWIN  &  Co. 


Cr. 


1905 

1905 

Nov. 

10 

Mdse.,  60  days 

320 

April 

4 

Cash 

450 

Dec. 

23 

"       90    " 

185 

May 

16 

Draft,  60  da. 

95 

1906 

1906 

Mch. 

12 

"       30    " 

236 

90 

June 

3 

Note,  1  mo. 

120 

June 

4 

"       10    " 

468 

60 

July 

20 

Cash 

186 

SO 

July 

3 

15     " 

241 

50 

458.  To  find  the  date  of  payment  of  the  net  proceeds  of  a 
consignment. 

The  sales  constitute  the  credit  side  of  the  account.  The  ex- 
penses of  the  consignment  (freight,  storage,  commission,  etc.), 
and  the  money  advanced  before  the  account  is  closed,  constitute 
the  debit  side  of  the  account. 

Find  the  average  due  date  of  the  sales,  and  take  this  date  as 
the  due  date  of  the  commission.  Find  the  due  date  of  settlement 
the  same  as  in  previous  problems. 

1.  When  are  the  net  proceeds  of  the  following  account  sales 
due? 

Account  Sales  of  Pork.  Nashville,  Tenn.,  Sept.  1,  1905. 

Sold  for  account  of  Swift  &  Co.,  Chicago,  111. 


1905 

July 

3 

25  bbls.  Mess  Pork  @  $12.80,  30  days. 

*** 

** 

a 

23 

45      "      Mess   Pork   @  $12.60  cash. 

*** 

** 

Aug. 

6 

40       "      Prime   Pork    @   $13,   20  days. 

*** 

*# 

« 

17 

30             Prime  Pork  @  $12.85,  10  days. 

*** 

## 

#### 

** 

CHARGES 

July 

1 

Freight 

71 

40 

« 

1 

Cash  advanced 

250 

Commission  (due  )                            4# 

*** 

#* 

****• 

** 

Net  proceeds  (due  ) 

*#** 

** 

2.  When  will  the  net  proceeds  of  the  following  account  sales 
be  due? 


EQUATION  OF  ACCOUNTS 


309 


Account   sales  of  flour  sold  for  account  of  Geo.  F.  Snyder  & 
Co.,  Minneapolis,  by  Davis  &  Co. 


1905 

May 

6 

110   bbls.   XX   Flour   @  $5.90,  10  davs. 

*** 

** 

" 

30 

90       "      XX   Flour   @   $6,           5#  off 

**# 

** 

June 

16 

76       "      XXX   Flour  @  $6.05,  20  davs. 

*#* 

** 

30 

125       "      XXX   Flour  @  $6.10  cash. 

*** 

** 

*#*# 

*# 

CHARGES 

May 

2 

Freight 

86 

12 

• 

6 

Accepted  Snyder's  draft,  15  days 

400 

" 

25 

Cooperage 

12 

June 

30 

Storage 
Commission  (due  )                       3^  % 

23 

** 

80 
** 

Net  proceeds  (due  ) 

**** 

** 

After  having  ascertained  the  date  at  which  the  Net  Proceeds 
of  a  consignment  is  due,  to  find  the  cash  balance  at  any  later  date, 
add  the  interest  to  the  Net  Proceeds  for  the  intervening  time. 

3.  Find  the  date  of  settlement  of  the  net  proceeds,  and  the 
cash  balance  on  September  1,  1905 — 1%. 

Account  sales  of  produce  by  John  Mason,  for  account  of  J.  B. 
Hayes,  Detroit,  Mich. 


1905 
March 

April 
May 

March 
May 

12 
16 
23 
4 

6 

3 
3 
5 

6 

300  doz.  Eggs  @  15  cts.,  30  days 
700  Ibs.  Butter  @  21^  cts.,  10  days 
210  doz.  Eggs  @  14^  cts.,  cash 
200  Ibs.  Butter  @  22^  cts.,  2$  off 
290  doz.  Eggs  @  15  cts.,  10  days 

CHARGES 

Freight 
Cartage 
Cash  advanced 
Storage  from  March  3 
Commission  (due  )                4# 

Net  proceeds  (due  ) 

** 
*** 

** 
** 
** 

**** 

** 

90 
7 
150 
31 

*** 

60 
90 

50 

**** 

** 

**** 

4.  Find  the  average  due  date  of  sales;  the  true  date  of  set- 
tlement of  the  proceeds  and  the  cash  balance  on  August  10,  1905 


310 


NEW   BUSINESS   ARITHMETIC 


Sales  of  A.  B.  Wilson  &  Co.,  for  account  of  S.  R.  Lockwood  & 
Co.,  Springfield,  111. 


1905 

Feb. 

14 

105  bbls.  Potatoes  @  $1.40,  10  days 

*** 

** 

March 

2 

80     "     Apples  @  $2.80,  3#  off 

*** 

** 

« 

30 

120      "     Apples  @  $2.75,  20  days 

*** 

** 

April 

3 

75      "     Potatoes  @  $1.35,  30  days 

#*# 

** 

u 

16 

20            Potatoes  @  $1.45,  cash 

*** 

** 

**** 

** 

CHARGES 

Feb. 

10 

Freight 

64 

28 

M 

10 

Drayage 

11 

50 

« 

15 

Accepted  their  draft  at  10  days 

200 

« 

19 

Cooperage 

6 

20 

April 

16 

Storage  from  Feb.  10 

15 

Commission  (due  )             4l/2% 

*** 

** 

**** 

** 

Net  procesds  (due  ) 

**** 

** 

CASH  BALANCE 

459.  Cash  Balance  is  the  amount  of  money  which  will  settle 
an  account  on  a  given  date.  Cash  balance  is  the  difference  be- 
tween the  two  sides  of  an  account,  with  the  interest  added  to  all 
past,  due  items. 

In  settling  mercantile  accounts  interest  is  not  always  reckoned.  This 
is  regulated  by  previous  agreement  and  also  by  custom.  When  interest 
is  charged  it  is  calculated  from  the  time  the  account  is  due. 

The  cash  balance  of  an  account  may  be  found  by  either  the  product, 
or  interest  method,  but  the  latter  is  preferable. 

1.  Find  the  cash  balance  July  3,  1905,  on  the  following  ac- 
count, interest  at  6%. 


Dr. 


Williams  &  Brown  in  account  with 
J.  R.  Wood 


Cr. 


1905 

1905 

Jan. 

24 

Mdse  20  da. 

168 

50 

Apr. 

2 

Cash 

150 

Mar. 

1 

Mdse  15  da. 

79 

20 

May 

6 

Note  13  da. 

270 

50 

May 

4 

Mdse  10  da. 

864 

80 

ft 

6 

Cash 

63 

50 

tr 

23 

Mdse 

204 

50 

June 

2 

Cash 

100 

DUE.                     ITEMS.       DAYS.  INTEREST. 

DUE.                  ITEMS.         DAYS.  INTEREST. 

Feb.  13,    $168.50  HO     $3.93 

Apr.  2,       $150.00     92     $2.30 

Mar.  16,        79.20  109       1.44 

May  19,       270.50     45       2.03 

May  14,      364.80     50       3.04 

May  6,           63.50     58         .61 

May  23,      204.50     41       1.39 

June  2,         100.00     31         .52 

$817.00             $9.80 

$584.00            $5.46 

584.00               5.46 

$233.00  +  $4.34  =  $237.34 

EXPLANATION. — If  J.  R.  Wood  had  paid  nothing  before  July  3,  he 
would  owe  the  items  on  the  Dr.  side  of  the  account  and  also  the  interest 
on  them  to  July  3  amounting  to  $9.80 ;  but  as  he  paid  some  amounts  before 
that  date  he  is  entitled  to  credit  for  the  amount  paid  and  also  the  interest 
upon  them  from  the  date  of  payment  until  July  3,  amounting  to  $5.46. 
This  interest  deducted  from  $9.80  leaves  $4.34  the  net  amount  of  interest 
added  to  the  balance  of  the  account  gives  the  total  due,  or  cash  balance  due 
on  July  3,  1905,  $237.34. 

811 


312 


NEW    BUSINESS   ARITHMETIC 


NOTES. — 1.  When  the  balance  of  interest  is  on  the  same  side  of  the 
account  as  the  balance  of  items,  it  is  added  to  the  balance  of  the  items; 
when  it  is  on  the  opposite  side  it  is  subtracted  from  the  balance  of  the 
items. 

2.  In  computing  interest  regard  fractional  parts  of  a  dollar  less  than 
half  as  nothing,  and  equal  to  or  greater  than  half  as  one  dollar.  But  in 
adding  these  items  the  exact  cents  must  be  taken. 

2.  Find  the  cash  balance  on  October  30,  1905,  at  6%  interest. 


Dr. 


E.  T.  NICHOLS. 


Cr. 


1905 

1905 

Mar. 

5 

Mdse. 

146 

30 

May 

1 

Cash 

100 

April 
May 

3 
17 

10  days 

"      20    " 

561 

328 

40 
80 

June 

4 
30 

Note,  30  d" 
Check 

165 
75 

50 

June 

4 

11      15    " 

196 

50 

July 

5 

Cash 

290 

50 

July 

10 

"      $600 

3  &  5#  off 

*** 

** 

3.  Find  the  cash  balance  on  September  1,  1906,  at  5%  interest. 

Dr.                                  E.  J.  COLLINS.                                   Cr. 

1905 

1906 

Aug. 
Dec. 

1906 

30 
16 

Mdse.  90  days 

"      30    " 

278 
123 

25 

Jan. 

1 

Note,  $250  with  in- 
terest   for  8  mo. 
10    da.,    at  8  per 

*** 

** 

Feb. 

Mar. 

3 
21 

"      $960 
5  &  5%  off 

"      $820, 

*** 

** 

Mar. 
April 

12 
2 

Note,  2  mo. 
Mdse.  $140, 

2$  off 

540 
*** 

** 

April 

6 

3  &  4#  off 
"      20  days 

*** 
378 

15 

May 

10 

"      $310, 
5  &  6%  off 

*** 

** 

May 

1 

"    $260,  4*  off 

*** 

** 

" 

20 

Cash 

180 

4.  Find  the  cash  balance  on  January  1,  1906,  at  6%  interest. 

Dr.                                    I.  K.  JAMES.                                     Cr. 

1905 

1904 

Jan. 

13 

Note,  60  days 

225 

June 

4 

Mdse.,  3  mo. 

196 

30 

" 

28 

Draft,  33    " 

172 

15 

Sept. 

10 

2     " 

211 

40 

May 

1 

30 

Check 
Cash 

86 
123 

40 
45 

1905 

Jan. 

1 

$440, 

June 

10 
30 

Note,  13     " 
Cash 

75 

100 

Mar. 

1 

2  &  4%  off 
Mdse,  $175, 

*** 

5^  off 

*** 

** 

June 

1 

30  da. 

280 

26 

10    " 

192 

80 

PARTNERSHIP 

460.  A  Partnership  is  an  association  of  persons  who  join 
their  capital,  labor  and  skill — for  the  purpose  of  conducting  some 
business,  and  who  agree  to  divide  the  profits  and  bear  the  losses 
in  certain  proportions. 

The  business  association  is  called  a  Finn  or  House. 

461.  Partners  are  the  persons  forming  the  association.   They 
are  active  or  silent,  general  or  special. 

1.  An  active  partner  is  one  who  takes  an  active  part  in  the 
management  of  the  business. 

2.  A  silent  partner  is  one  who  furnishes  capital,  and  shares  in 
the  profits  and  losses,  but  takes  no  active  part  in  the  management 
of  the  business. 

3.  A  general  partner  is  one  who  is  responsible  for  the  debts 
of  the  company  to  the  amount  of  his  entire  property. 

4.  A  special  partner  is  one  whose  responsibility  is  limited  to  a 
certain  amount  specified  in  the  written  articles  of  partnership. 

462.  The  Capital  is  the  money  or  other  property  invested 
in  the  business. 

463.  Resources,  sometimes  called  Assets,  of  a  firm  are  its 
entire  property  including  all  debts  due  the  firm. 

464.  Liabilities  of  a  firm  are  its  debts. 

465.  Net  Capital  of  a  firm  is  the  excess  of  its  resources  over 
its  liabilities. 

466.  Net  Insolvency  of  a  firm  is  the  excess  of  its  liabilities 
over  its  resources. 

313 


314  NEW   BUSINESS   ARITHMETIC 

467.  Net  Investment  of  a  partner  is  the  amount  of  the  capital 
of  the  firm  which  he  has  invested  less  the  amount  he  may  have 
withdrawn  from  the  business. 

468.  Net  Gain  of  a  firm  is  the  excess  of  total  gains  over  total 
losses. 

469.  Net  Loss  of  a  firm  is  the  excess  of  total  losses  over  total 
gains. 

The  Gain  is  found  by  subtracting  the  investment  from  the 
net  worth  at  closing.  The  loss  is  found  by  subtracting  the  net 
worth  at  closing  from  the  investment. 

Gains  and  losses  are  divided  between  the  partners  according  to  agree- 
ment, but  in  the  absence  of  any  express  agreement,  it  is  understood 
that  the  partners  are  to  share  equally  in  gains  or  losses. 

Partnerships  are  General,  and  Special  or  Limited. 

470.  A  General  Partnership  is  one  in  which  each  partner  is 
liable  for  the  debts  of  the  firm  to  the  full  extent  of,  not  only  his 
interest  in  the  business,  but  his  private  property  also. 

471.  A  Special  or  Limited  Partnership  is  one  having  one  or 
more  general  partners  and  one  or  more  special  partners.     Each 
special  partner  is  liable  for  the  debts  of  the  firm  only  to  the  ex- 
tent of  his  investment,  and  his  private  property  cannot  be  taken  to 
pay  firm  debts. 

The  laws  relative  to  special  or  limited  partnerships  in  most  states  re- 
quire : 

1.  That    written    articles    of    copartnership    shall    be    drawn,    signed 
by  all  the  partners,  specifying  the  general  and  special  partners,  and  the 
amount  invested  by  each,  which  articles  must  be  recorded  in  the  public 
records  of  the  county. 

2.  There  must  be  at  least  one  general  partner,  who  shall  manage  the 
business  and  who  shall  be  liable  for  the  debts  of  the  firm  the  same  as  in 
a  general  partnership. 

3.  Special  partners  shall  take  no  active  part  in  the  management  of  the 
business. 

4.  The  investment  of  each  special  partner  must  be  fully  paid  in. 
An  omission  of  any  of  these  conditions  makes  the  partnership  gen- 


PARTNERSHIP  315 

eral  and  all  of  the  partners  equally  liable  for  debts  the  same  as  in  a  general 
partnership. 

472.  The  investment  and  the  resources  and  liabilities  at  clos- 
ing being  given  to  find  the  gain  or  loss. 

1.  A  firm  invested  cash  $2300;  merchandise  $1180;  other  per- 
sons' notes  $1500;  accrued  interest  $20.    At  closing  the  resources 
were  cash  $3900;  merchandise  $362;  notes  due  $1698;  accrued 
interest  $49.20 ;  personal  accounts  due  $991.80.    Find  the  gain. 

NOTE. — From  the  total  resources  at  closing  subtract  the  total  invest- 
ment. 

2.  A  and  B  formed  a  partnership  for  a  year.    A  invested  cash 
$1600;  notes  $380;  Lyman's  account  $120.     B  invested  merchan- 
dise $1280;  notes  $415;  horse  and  wagon,    valued    $205.     The 
firm  had  at  the  close  of  the  year  cash  $3200 ;  merchandise  $312.40 ; 
notes  due  $480.20 ;  personal  accounts  $1049.90.     How  much  did 
they  gain  ? 

3.  Sanders  and  Reed  formed  a  partnership  and  invested  as 
follows:     Cash  $3300;  dry  goods  invoiced  at  $600  with  a  dis- 
count of  10  and  5% ;  Byrne's  note  of  $720,  that  had  been  on  in- 
terest 4  months  at  9%;  personal  accounts  due  $629.10;  fixtures 
$216.50.     They  had  at  closing  $4217.20  cash  in  the  bank,  $370 
cash  in  the  safe;  $490  worth  of  fixtures;  $1200  worth  of  mer- 
chandise.   Did  they  gain  or  lose  and  how  much  ? 

4.  Smiley,  Richards  and  Bloomer  formed  a  partnership  for 
two  years.    Smiley  invested  cash  $1000 ;  real  estate  $1800.    Rich- 
ards invested  a  stock  of  groceries  $2000  with  3%  and  5%  off; 
cash  $1000.     Bloomer  invested  cash  $1250;  office  fixtures  $160; 
horse  and  wagon,   $270;   Brown's   note   of  $450,   with  accrued 
interest  for  5  months  10  days  at  10%.    The  firm  sold  all  its  prop- 
erty at  the  end  of  two  years  and  had  $10699.28  cash.     Find  the 
gain. 

5.  A  invested  $1250  cash;  store  valued  at  $2150;  personal 
accounts  $382.50.     He  owed  a  note  of  $320  which  the  firm  as- 
sumed.    B  invested  $3180  cash;  office  safe  valued  at  $145.     He 
owed  personal  accounts  $653.30  which  the  firm  assumed.     C  in- 


316  NEW   BUSINESS   ARITHMETIC 

vested  his  stock  of  clothing,  invoiced  at  $2700  on  which  he  al- 
lowed a  discount  of  4%.  The  resources  at  closing  were  cash 
$6394.25;  merchandise  $1746.35;  store  $2000;  office  safe  $130; 
Reeve's  note  of  $980  which  had  been  on  interest  for  114  days  at 
9%.  Was  there  a  gain  or  loss  and  how  much?  What  was  each 
partner's  portion  of  the  gain  or  loss  A  sharing  tV,  B  1*1  and  C  A? 
NOTE. — Subtract  the  debts  of  the  partners,  which  were  assumed  by 
the  firm  from  their  investment  to  find  the  net  worth  at  the  beginning. 

6.  Smails,  Dorsey,  Adams  and  Piper  formed  a  partnership  to 
share  the  gains  and  losses  equally,  and  invested  as  follows : 
Smails  invested  cash  $3000 ;  10  shares  bank  stock  worth  $126  per 
share.  Dorsey  invested  his  stock  of  boots  and  shoes  valued  at 
$4000.  Adams  invested  cash  $1900;  a  real  estate  mortgage  of 
$2000  with  accrued  interest  for  6  months  and  20  days  at  8%. 
Piper  invested  his  store  and  lot  valued  at  $3750.  During  the 
time  of  partnership  Smails  withdrew  cash  $300  and  merchandise 
$92.40.  Adams  withdrew  cash  $217.20.  Dorsey  withdrew  mer- 
chandise $37.50.  Piper  withdrew  cash  $226.  The  property  at 
closing  was  cash  $17294.10;  outstanding  notes  $2432.15;  per- 
sonal accounts  $234.90.  Did  the  firm  gain  or  lose  and  how  much? 
What  was  each  partner's  share  of  the  gain  or  loss  ? 

NOTE. — The  withdrawals  of  the  partners  must  be  added  to  the  re- 
sources at  closing  to  find  total  amount  as  if  nothing  had  been  drawn. 

473.  The  investment,  the  resources  and  liabilities  at  closing 
and  the  proportion  in  which  the  partners  share  the  gains  or  losses 
being  given,  to  find  each  partner's  interest  in  the  concern  at  clos- 
ing. 

1.  A  and  B  are  partners.  A  is  to  share  f  of  the  gain  or  loss, 
and  B  f .  At  the  close  of  business  the  following  is  shown  to  be 
the  condition  of  their  affairs,  viz. :  Cash  on  hand  $2680.  Bills 
receivable  on  hand  $3620.  Five  shares  Bank  stock  valued  at  $520. 
House  and  lot  valued  at  $6000.  Wilson  &  Co.  owe  on  account 
$1800.  The  firm  owe  on  notes  outstanding  $2840.  They  owe  C. 
W.  Lane  on  account  $890.  A  invested  $4610.  B  invested  $4860. 
What* is  A's  interest  in  the  concern?  What  is  B's  interest  in  the 
concern  ? 


PARTNERSHIP 


317 


SOLUTION 


RESOURCES 

Cash  on  hand $2680 

Bills  Receivable 3620 

Bank  Stock 520 

House  and  Lot 6000 

Wilson  Co.  owe..  1800 


Net  gain 

5)1420      net  gain. 
284  i  net  gain. 
3 

$852  B's  f  net  gain. 
568  A's  f  net  gain. 


$14620 
13200 

$1420 


LIABILITIES 

Notes  unpaid $2840 

Due  C.  W.  Lane 890 

A  invested 4610 

B  invested . .  4860 


$13200 

A  invested 4610 

A  f  net  gain 568 

A   present    interest    in 

concern $5178 

B  invested 4860 

B  |  net  gain 852 

B    present    interest    in 
concern..  .   $5712 


2.  C,  D  and  E  formed  a  copartnership,   each   to   share   £    of 
the  gains  and  losses.     At  the  close  of  the  year  the  resources  and 
liabilities  were  as  follows :    Cash  in  bank  $3600.     Stock  of  goods 
in  store  $10680.     Bills  receivable  on  hand  $5820.     Mining  stock 
valued  at  $8730.     Stock  in  Third  National  Bank  $2850.     Store 
building  and  lot  valued  at  $28000.     Account  due  from  Lyons  & 
Co.  $865.30.    W.  C.  Anderson  owes  the  firm  $1630.    Wm.  D.  Barr 
owes  the  firm  $178.50.    The  firm  owe  on  their  notes  outstanding 
$4380.     They  owe  Davis  &  Morse  $1325.     C  invested  $12650. 
D  invested  $12400.     E  invested  $12250.     What  is  each  partner's 
interest  in  the  concern  at  closing? 

3.  Jones,  Brown  and  Smith  entered  into  a  copartnership,  they 
to  share  gains  and  losses  as  follows :    Jones  f ,  Brown  f  and  Smith 
J.     After  conducting  business  one  year  the  following  are  the  re- 
sources and  liabilities :     Cash  on  hand  $3625.     Mill   and  other 
real  estate  $8342.     Bills  receivable  $1230.     G.  W.  Samuels  owes 
the  firm  $375.    A.  W.  Dakin  owes  the  firm  $637.    L.  M.  Painter 
owes  the  firm  $1632.     Stock  in   Globe   National   Bank  $2430. 
Brown  has  withdrawn  during  the  year  $350.  Smith  has  withdrawn 
$180.     The  firm  owe  on  notes  outstanding  $5720.     They  owe  H. 


318  NEW  BUSINESS   ARITHMETIC 

B.  Conant  $1300.  Jones  invested  $3600.  Brown  invested  $3000. 
Smith  invested  $2800.  What  is  each  partner's  interest  at  clos- 
ing? 

4.  F,  G,  H  and  I  are  partners.     They  share  the  gains  and 
losses  as  follows :     F  and  G  each  T32,    H    T\    and    I    ^.     After 
doing  business  one  year  they  find  the  following  resources  and  lia- 
bilities:  Cash  in  bank  $4230.     Cash  in  safe  $320.     Merchandise 
in  store  $12840.     Goods  shipped  away  on  consignments  $1640. 
Real  estate  $6400.    Horses  and  wagons  $1000.    Wheat  and  corn 
$930.     Lumber    $1730.     Accounts    receivable    $2340.      F     has 
withdrawn  from  the  business    $350.     H    has    withdrawn    $260. 
The   liabilities  of  the   firm  are   notes   outstanding  $3860.     Due 
Marshall  Field  &  Co.  $820.    Due  John  W.  Norris  &  Co.  $135.40. 
Due  N.  K.  Fairbank  $216.30.     F  invested  $5834.     G  invested 
$6243.     H  invested  $6000.     I    invested    $5635.     What    is    each 
partner's  interest   in   the   concern  at  closing? 

5.  There  are   four  partners  in  a  concern,   O,   P,  Q  and  R. 
Each  partner  to  share  £  of  the  gains  or  losses.     At  dissolution 
there  is:     Cash  on  hand  $6820.     Bills  receivable  $8922,     C.  B, 
&  Q.  R.  R.  stock  $4500.     Deposit  in  National  Bank  Commerce 
$3680.    O  has  drawn  from  the  concern  $860.    P  has  drawn  $575. 
Q  has  drawn  $630.     R  has  drawn    $452.     The    liabilities    are: 
Notes  and  Acceptances  outstanding  $3680.     Balance  in  favor  of 
Smith  &  Co.  $1264,  in  favor  of  Collins,  Downing  &  Co.  $860, 
Geo.  Warner  $575.     O  invested  $5590.     P  invested  $5322.     Q 
invested  $5540.     R  invested  $5228.     What  has  been  the  net  gain 
or  loss?    What  is  each  partner's  interest  in  the  business? 

474.  The  investment  and  the  gains  and  losses  being  given, 
to  find  the  capital  at  closing. 

1.  A  and  B  are  partners,  sharing  the  gains  and  losses  equally. 
A  invested  $2865.  B  invested  $3000.  The  gain  during  the  year 
was  $1860  on  Merchandise.  $76.20  Interest.  The  loss  was 
$246.15  Expenses.  $2.20  Exchange.  $14.13  Discount  on  notes 
paid  before  they  were  due.  Find  the  net  gain,  and  the  net  capital 
.t  closing,  also  each  partner's  interest  at  closing. 


PARTNERSHIP  319 

SOLUTION 


B 


Balance       $3701.861  Investment       $2865  Balance       $3836.86\  Investment       $300C 

I  Gain  836.86  I  Gain  836.86- 

Profit  and  Loss 


Expense $246.15 

Exchange 2.20 

Discount 14.13 

A's  gain 836.86 

B's  gain 836.86 

$1936.20 


Mdse $1860 

Interest 76.20 


$1936.20 


A's  interest  at  closing $3701.86 

B's  interest  at  closing 3836.86 

Firm's  capital  at  closing $7538.72 

2.  Parker,  Hammond  and  Siders  formed  a  partnership  for  one- 
year,  sharing  gains  and  losses  equally.     Parker    invested    cash 
$3600,  and  withdrew  during  the  year  $230.     Hammond  invested 
cash  $1200;  Merchandise  $1480;  Notes  $365;  Accounts  due  him 
$240.     He  withdrew  during  the  year  $176.     Siders  invested  real 
estate  $1975 ;  Cash  $640 ;  Potter's  note  of  $220  that  had  been  on 
interest  at  1%  for  1  year  and  6  months.     They  gained  $2468.45 
on  Merchandise  and  $29  interest  on  notes.    The  loss  was  $290.50 
expenses  for  running  the  store.     What  was  the  interest  of  each 
partner,  and  the  capital  of  the  firm,  at  closing? 

3.  Stewart,   Nevins  and   Barnard   are   partners   in   business. 
Stewart  is  to  share  f  of  the  gains  or  losses,  Nevins  f  and  Barnard 
J.    Stewart  invested  Dry  Goods  valued  at  $2250  with  2  and  10% 
off;  White's  Note  of  $1248,  due  in  6  months,  on  which  he  allows 
true  discount  at  8%.     Nevins  invested  Cash  $2500;  Personal  Ac- 
counts $426.80.     Barnard  invested  Store  and  Lot  worth  $3250. 
During  the  term  of  partnership  Stewart  withdrew  Merchandise 
$68.20  and  invested  $750  Cash.     Nevins  made  an  additional  in- 
vestment of  $1000  Cash  and  withdrew  $110  worth  of  Merchan- 
dise.    Barnard  withdrew  $420  Cash.     The  gains  were  $1968  on 
Merchandise,  $220  Rent  for  part  of  store,  $23.10  Interest.     The 
losses  were  $360  Expenses,  $33.95  on  Personal  Accounts.     What. 


320  NEW    BUSINESS    ARITHMETIC 

was  the  net  worth  of  each  partner,  and  the  firm's  net  capital,  at 
closing  ? 

4.  A,  B,  C  and  D  formed  a  copartnership  for  one  year.  A  is 
to  share  j  of  the  profits  or  losses,  B  f ,  C  -J  and  D  the  remainder. 
On  January  1,  A  invested  cash  $1200;  Merchandise  $280;  Notes 
$760;  Personal  Accounts  due  him  $316.90.  On  March  3,  he 
withdrew  $600.  On  January  1,  B  invested  Merchandise  $2200; 
on  May  1,  he  invested  $400  Cash  and  withdrew  $23.15  worth  of 
Merchandise.  On  January  1,  C  invested  Cash  $1800;  Notes 
$500  with  accrued  Interest  $17.80;  Personal  Accounts  due  him 
$176.40.  On  January  1,  D  invested  Cash  $2000;  Merchandise 
$300  with  4  and  5%  off.  On  June  16,  he  invested  $620  Cash. 
The  losses  were  $264.18  for  Running"  Expenses,  other  than  the 
rent  which  was  $275;  3%  of  Personal  Accounts  of  $3729.70. 
The  gains  were  $2394.13  on  Merchandise;  $23.66  Interest.  Find 
the  net  worth  at  closing  of  each  partner  and  also  the  firm. 

475.  To  find  each  partner's  gain  or  loss  when  the  capital  of 
the  several  partners  is  invested  for  the  same  length  of  time,  and 
they  are  to  share  gains  and  losses  in  proportion  to  the  capital  in- 
vested. 

1.  A,  B  and  C  enter  into  copartnership  in  the  grocery  busi- 
ness for  a  term  of  2  years.    A  invested  $3600,  B  invested  $4200, 
C  invested  $2400.     At  the  close  of  the  partnership  term  it  was 
found  that  the  net  profits  of  the  business  had  been  $3570.    What 
was  each  partner's  portion  of  the  profits? 

SOLUTION 

$3600  +  $4200  +  $2400  =  $10200  total  investment. 

$3570  -^  $10200  =  .35  or  35%  the  rate  of  gain. 

$3600  X  .35  =  $1260  A's  gain. 

$4200  X  -35  =  $1470  B's  gain. 

$2400  X  .35  =  $840  C's  gain. 

2.  Two  speculators  A  and  B  operated  together  in  buying  and 
selling  cattle.  A  made  purchases  amounting  to  $2735,  and  paid 
expenses  amounting  to  $484.60.     B  made  purchases  amounting 
to  $3687.50  and  paid  expenses  amounting  to  $387.30.     The  cat- 
tle were  sold  by  B  for  $8214.75.    What  is  the  gain  or  loss?    How 


PARTNERSHIP  321 

will  the  partners  settle  between  them,  the  gains  or  losses  to  be 
shared  in  proportion  to  their  investments? 

3.  Fuller,  Irwin  and  Diers  formed  a  partnership  for    1    year 
and  invested  as  follows :     Fuller  invested  $1500  Cash.     Irwin  in- 
vested Merchandise  $2000;  Notes  $200.     Diers  invested,  Store 
$1250;  Notes  $350;  Personal  Accounts  $200.     Their  resources 
at  closing  were :    Cash  $3160.35  ;  Merchandise  $2500 ;  Notes  $320 
with  Interest  due  $8.75 ;  Personal  Accounts  $335.90.     The  gains 
were  divided  in  proportion  to  the  partner's  investments.     What 
was  the  total  gain  and  each  partner's  gain? 

NOTE. — Find  the  net  gain  or  net  loss  by  taking  the  difference  between 
the  investments  and  the  resources  at  closing,  then  proceed  as  in  the 
previous  problem. 

4.  A,  B  and  C  engaged  in  business  on  August  1,  1901.     A  in- 
vested $2400,  B  invested  $1700,  C  invested  $2900.     On  August 
1,  1902,  the  resources  were  as  follows :     Cash  $3850 ;  Merchan- 
dise $2690 ;  Notes  $1800 ;  Personal  Accounts  $862.40 ;  Horse  and 
Wagon  $285.     The  liabilities  were  Personal  Accounts  $192.40, 
Bills  payable  $260.     During  the  year  A  withdrew  $90 ;  B  $100 ; 
C  $85.     The  gains  were  divided  in  proportion  to  the  investment. 
What  was  the  gain  of  each  ? 

NOTE. — The  withdrawals  of  partners  are  resources  to  the  business  the 
same  as  personal  accounts  of  other  parties. 

5.  Jennings,  Fuller  and  Clark  engage  in  business  for  a  term 
of  two  years.     Jennings   invests   $3000;   Fuller   invests   $1980; 
Clark  invests  $2370.     On  closing  their  books  they  found  their 
gains  as  follows :     On  Merchandise  $3194.20 ;  Interest  on  Bills 
Receivable  $93.60 ;   Discount  on  their  Notes    paid    before    due 
$28.70.     The  losses  were  Running  Expenses  $150;  Rent  $200, 
Personal  Accounts  $26.50.     What  was  the  net  gain  of  each,  the 
gain  being  shared  according  to  their  investments? 

6.  F,  G  and  H  engage  in  the  grocery  business,  agreeing  to 
share  gains  and  losses  in  proportion  to  their  investments.     F  in- 
vests $1600;  G  invests  $1800;  H  invests  $2000.     At  the  end  of 
the  partnership  term  they  find  their  gains  as  follows:     On  Mer- 

21 


322  NEW    BUSINESS    ARITHMETIC 

chandise  $1480 ;  Discount  on  bills  paid  before  due  $148.30.  The 
losses  were:  Expenses  $540;  Bad  Debts  $78.50.  What  was 
the  net  gain  and  each  partner's  share  thereof? 

476.  To  find  each  partner's  gain  or  loss  when  the  capital  of 
the  several  partners  is  invested  for  different  lengths  of  time,  and 
they  are  to  share  gains  and  losses  according  to  the  amount  of 
capital  invested  and  time  it  is  employed. 

1.  On  January  1,  A  and  B  formed  a  partnership  for  one  year. 
A  invested  $1700  on  January  1,  and  $720  on  March  1.  He  with- 
drew $600  on  June  1.  B  invested  $2000  on  January  1,  and  $800 
on  April  1.  He  withdrew  $750  on  May  1.  The  net  gain  was 
$972.  What  was  the  gain  of  each  partner? 

SOLUTION 

Find  the  time  in  months  from  the  date  of  each  investment  and 
withdrawal  to  the  end  of  the  year. 
A  invested  $1700  X  12  =  $20400 
A  invested      720  X  10  =      7200 

A  withdrew  600  X      7  =^200  |  use  of  ^340°  for  l  ™' 
$23400   -J-  12  =  $1950,     A's  average  investment  for  1  year. 
B  invested  $2000  X  12  =  $24000 
B  invested      800  X    9  =      7200 


B  withdrew  750   X    8  =      — "  '  use  of  $8520°  for  l  mo" 


$25200  -f-  12  =  $2100,  B's  average  investment  for  1  year. 
$1950  +  $2100  =  $4050  total  investment  for  1  year. 
$972  -r-  4050  =  .24  or  24%  gain  on  investment. 
$1950  X  .24  =  $468  A's  gain. 
$2100  X  .24  —  $504  B's  gain. 

2.  Hammond  and  Cowles  formed  a  partnership  to  run  for  1 
year  from  September  10,  1905.  Hammond  invested  $3500  on 
September  10,  $1800  on  December  10,  and  $600  on  March  10, 
1906.  Cowles  invested  $4200  on  September  10,  and  $900  on  Jan- 
uary 10,  1906.  The  net  gain  of  the  firm  was  $1990.  What  was 
each  partner's  gain? 


PARTNERSHIP  323 

3.  On  March  1,  1905,  Manning,  Miller  and  Collins  formed  a 
partnership  for  10  months.     Manning  invested  $1400  on  March 
1,  and  $1250  on  June  1.     Miller  invested  $1760  on  March  1,  and 
$2400  on  May  1.     Collins  invested  $2100  on  March  1,  and  $800 
on  August  1.     The  firm  gained  $5500.80.     What  was  each  part- 
ner's gain? 

4.  F.  M.  Tyler,  H.  F.  Brady  and  P.  W.  Hess  formed  a  part- 
nership on  July  1,  1905,  for  1  year.    Tyler  invested  $4600  on  July 
1  and  $1200  on  December  1.    He  withdrew  $1800  on  February  1, 
1906.     Brady  invested  $7400  on  July  1,  and  withdrew  $2400  on 
January  1,  1906.     Hess  invested  $6500  on  July  1  and  $3000    on 
March   1,   1906.     The  firm's  net  loss   for  the  year  was   $1245. 
What  was  the  loss  of  each  partner  ? 

5.  On  May  18,  1905,  A  and  B  formed  a  partnership  for  1  year. 
A  invested  $4000  on  May  18  and  $2700  on  September  18.    B  in- 
vested $3500  on  May  18  and  $1800  on  October  18.     A  withdrew 
$1900  on  November  18  and  $600  on  January  18,  1906.     B  with- 
drew $900  on  July  18  and  $2100  on  February  18,  1906.    The  net 
gain  of  the  firm  was  $1589.50.    Find  the  gain  per  cent,  on  the  in- 
vestment and  each  partner's  net  gain. 

6.  On  January  1,   1905,  A,  B  and  C  formed  a  partnership 
which  was  dissolved  August  20,  1905.     At  the  beginning  of  the 
business  each  invested  $2500.     A  invested  $800  on  April  11.     B 
invested  $950  on  June  3.     C  withdrew  $500  on  May  30.    The  re- 
sources at  closing  were  cash  $8200,  Merchandise  $1650,  Notes 
$840.     Find  each  partner's  gain  or  loss,  there  being  no  liabilities 
other  than  the  investments. 

NOTE. — Count  the  exact  days  in  finding  the  time. 

477.  To  find  each  partner's  gain  or  loss  when  interest  is  al- 
lowed on  the  investments  and  charged  on  the  withdrawals. 

1.  On  April  1,  1905,  A  and  B  formed  a  partnership  for  one 
year.  A  was  to  share  -f%  of  the  gain  or  loss  and  B  TV  Each 
partner  was  to  receive  interest  on  his  investments  and  pay  interest 
on  his  withdrawals  at  6%.  The  net  gain  for  the  year  was  $2772. 
What  was  the  capital  of  each  on  April  1,  1906?  The  accounts 
on  April  1,  1906,  were  as  follows: 


324                                 NEW    BUSINESS    ARITHMETIC 

Dr.                                             A.                                               Cr. 

1905 

1905 

Sept. 

1906 

Jan. 

1 

1 

Cash 
Bills  Pay. 

1200 

800 

April 
Aug. 

1 

1 

Cash 
Mdse. 

8000 
3000 

Dr.                                             B.                                               Cr. 

1905 

1905 

Oct. 

16 

Cash 

900 

April 

1 

Cash 

15000 

SOLUTION 

Find  the  interest  on  each  investment  or  withdrawal  from  its 
date  to  the  date  of  settlement. 

A. 

Int.  on  $8000  for  1  yr.  =  $480. 
Int.  on  $3000  for  8  mo.  =  $120. 

$480  4-  $120  =  $600,  A's  credit  interest. 
Int.  on  $1200  for  7  mo.  =  $42. 
Int.  on  $800  for  3  mo.  =  $12. 

$42  +  $12  =  $54,  A's  debit  interest. 
$600  —  $54  =  $546,  A's  net  credit  interest 

B. 

Int.  on  $15000  for  1  yr.  =  $900,  B's  credit  interest. 
Int.  on  $900  for  5^  mo.  =  $24.75,  B's  debit  interest. 

$900  —  $24.75  =  $875.25,  B's  net  credit  interest. 

Carry  the  interest  items  to  the  Cr.  side  of  the  partner's  ac- 
counts and  Dr.  side  of  Profit  and  Loss.  Then  close  Profit  and 
Loss  account  and  credit  each  partner  with  his  portion  of  the  gain. 

PROFIT  AND  LOSS 


A's  interest 

$546  00 

Net  gain  

.  .  .  $2772.00 

B's  interest 

87525 

A's  net  gain 

56282 

B's  net  gain 

787.93 

I 

5 

^ 

2772.00 

] 

$2772.00 
3 

Cash  $1200 

Cash  .  .  . 

.$8000 

Cash       $900 

Cash  .  .  .$15000 

Bills  Pay,    800 
Netcap.,$10108.82 

Mdse.  .  . 
Interest 
Net  gain 

.  3000 
.     546 
.     562.82 

Netcap.,$15763.18 

Interest       875.25 
Net  gain      787.93 

PARTNERSHIP  325 

2.  Wakeham,  Griffin  and  Scallard  formed  a  partnership  on 
January  1,  1905,  for  1  year;  the  gains  and  losses  to  be  shared 
equally.     Interest   is  allowed   at   8%   on   all   sums   invested   and 
withdrawn.    On  January  1,  Wakeham  invested  $5000 ;  on  March 
1,  $1400.    He  withdrew  $600  on  June  1,  and  $300  on  September 
16.     On  January  1,  Griffin  invested  $7500;  on  June  16,  $1000. 
He  withdrew  $1500  on  March  1,  and  $450  on  July  1.     On  Jan- 
uary 1,   Scallard  invested  $9000;  on  July  1,  $1600.     He  with- 
drew $600  on  April   1.     They  gained  during  the  year  $11916. 
What  is  each  partner's  capital  on  January  1,  1906? 

3.  On  September  1,  1905,  A,  B,  C  and  D  formed  a  partner- 
ship for  16  months.     Interest  on  partners'  accounts  is  6%.    A  is 
to  share  J  of  the  gain  or  loss ;  B,  J ;  C,  £ ;    D,    J.     A    invested 
$4000  on  September  1 ;  B,  $6000  on  September  1,  $1500  on  March 
1;  C,  $8000  on  September  1,  $2000  on  August   16,   1906.     D, 
$10000  on  September  1,  $2400  on  January  1,  1906 ;  $900  on  June 
16,  1906.     B  withdrew  $900  on  January  1,  1906;  C,  $1800    on 
September  1,  1906 ;  D,  $1600  on  March  16,  1906 ;  $840  on  August 
1,  1906.    The  net  loss  during  the  partnership  was  $21792.    What 
was  each  partner's  net  credit  interest  and  net  capital  at  closing? 

4.  B.  A.  Harding,  E.  D.  Wilson  and  J.  P.  Parrel  formed  a 
partnership  for  one  year  from  August  20,  1905.    Harding  shared 
25%  of  the  gain  or  loss;  Wilson,  35%;  Farrel,  40%.     Interest 
was  allowed  on  all  investments  and  withdrawals  at  10%.    Hard- 
ing managed  the  business  at  a  salary  of  $1200.      At   the   begin- 
ning of  the  business  Harding  invested  $2500;  Wilson,  $3500  in 
Merchandise  with  3%  and  5%  off;  Farrel,  $4000.    On  January  1, 
1906,  Harding  withdrew  $800;  Wilson   invested  $1500;  Farrel 
invested  $500.    At  the  close  of  the  business  the  net  gain,  not  in- 
cluding A's  note  of  $300  which  Farrel  took  at  60%  of  its  face, 
was  $2786.40.     What  was  each  partner's  capital  at  closing,  no 
interest  being  allowed  on  the  salary  ? 

NOTES. — 1.    When  the  time  is  less  than  one  year  find  the  time  by 
counting  the  exact  number  of  days. 

2.     After  opening  the  Profit  and  Loss  Account,  charge  it  with  40% 


326  NEW    BUSINESS    ARITHMETIC 

of  A's  note,  and  charge  the  remaining  60%  to  Parrel,  and  credit  Profit 
and  Loss  with  full  amount. 

3.  Salaries  are  credited  to  the  partners  who  earn  them  and  charged 
to  Profit  and  Loss  account  the  same  as  interest. 

5.  A  and  B  formed  a  partnership  on  January  1,  1905.  A  is 
to  conduct  the  business  and  receive  65%  of  the  gain,  and  B, 
whose  time  is  not  employed,  is  to  receive  35%  of  the  gain.  On 
January  1,  A  invests  $4000;  on  May  3,  $1200,  and  withdraws 
$1600  on  June  15.  On  January  1,  B  invests  $3800;  on  March 
23,  $1800;  and  withdraws  $860  on  July  1.  Each  partner  is  to 
receive  8%  interest  on  the  amounts  he  invests,  and  pays  8%  in- 
terest on  all  amounts  which  he  withdraws;  the  interest  is  to  be 
adjusted  on  the  basis  of  each  receiving  ^  of  the  gain.  The  part- 
nership was  dissolved  on  August  25,  1905,  with  a  cash  resource 
of  $12000.  They  owed  $450  to  C,  which  B  assumes.  How  much 
of  the  cash  should  each  receive  ? 

NOTES. — 1.     Find  the  time  by  counting  exact  days. 

2.  Since  the  interest  is  not  adjusted  on  the  same  basis  as  other  profits, 
it  will  be  necessary  to  make  up  the  Profit  and  Loss  account  with  the 
interest  only,  and  find  remainder  of  gain  or  loss  from  the  resources  and 
liabilities. 

G.  A,  B  and  C  commenced  business  on  June  1,  1905,  with  re- 
sources as  follows:  A  invested  cash  $4000,  Merchandise  $1800, 
Fixtures  $250.  B  invested  Store  $4800,  Cash  $2750,  Personal 
Accounts  $800.  C  invested  Cash  $6000,  Notes  $1200,  Accrued 
Interest  $120.  The  firm  assumed  a  mortgage  of  $2500  on  the 
store,  and  A's  note  of  $1450.  A  was  to  share  30%  of  the  gain 
or  loss;  B,  35%;  C,  35%.  B  was  allowed  $800  per  year  for 
keeping  the  books.  On  June  1,  1906,  A  invested  $1500 ;  B  with- 
drew $1150;  C  invested  $2000.  On  January  1,  1907,  each  part- 
ner withdrew  $1000.  June  1,  1907,  the  partners  agreed  upon  a 
dissolution,  the  ledger  showing: 

RESOURCES.  LIABILITIES. 

Cash  $9786.20.          Notes  $940! 

Mdse.  $2314.30.          Interest  on  notes         $30. 

Notes  $1420.  Mortgage-balance    $1500. 

Real  estate         $4000.  B  for  salary  $1600. 

Personal  accts.  $2694.40. 


PARTNERSHIP  327 

Find  the  net  gain  or  loss  not  counting  interest  on  the  partners' 
accounts.  What  was  each  partner's  net  worth  at  closing,  if  in- 
terest was  allowed  at  9%  ?  (No  interest  allowed  on  B's  salary.) 

7.  J.  W.  White  and  H.  Murray  associating  together,  pur- 
chased a  flouring  mill  for  $8400,  in  which  White  holds  a  two- 
thirds  interest  and  Murray  one-third.  During  the  year  White 
paid  out  on  account  of  the  mill  $1548.26,  and  received  $4862.48. 
Murray  paid  out  $956  and  received  $2686.40.  A  settlement  is 
now  made,  the  mill  having  just  been  sold  for  $9000;  $4500  re- 
ceived, in  cash  and  the  balance  a  note  at  60  days  which  both  agree 
that  White  may  take  to  apply  on  his  account  at  20%  discount; 
and  the  $4500  is  then  properly  divided  between  them;  make  the 
division. 


INVOLUTION 

478.  A  Power  is  the  product  obtained    by    multiplying    a 
number  by  itself,  or  using  it  as  a  factor.    Thus,  9  =  3  X  3  is  the 
second  power  of  3 ;  27  =  3  X  3  X  3  is  the  third  power  of  3. 

479.  The  Exponent  of  a  power  is  the  number  denoting  how 
many  times  the  factor  is  repeated.     The   exponent    is   usually   a 
small  figure,  placed  at  the  right  and  a  little  above  the  factor.  Thus, 
32  signifies  that  3  is  to  be  raised  to  the  second  power ;  33  signifies 
that  3  is  to  be  raised  to  the  third  power,  etc. 

480.  The  Square  of  a  number  is  the  second  power  of  the 
number. 

481.  The  Cube  of  a  number  is  the  third  power  of  the  number. 

482.  Involution  is  the  process  of  raising   any   number   to   a 
given  power. 

From  the  preceding  we  have  the  following : 

To  Raise  Any  Number  to  a  Given  Power 

a.  Multiply  the  number  by  itself  until  it  has  been  used  as  often 
as  there  are  units  in  the  exponent  of  the  power. 

1.  Find  the  second  power  of  18. 

2.  What  is  the  third  power  of  54  ? 

3.  What  is  the  second  power  of  4.36  ? 

4.  Find  the  fourth  power  of  75. 

5.  What  is  the  sixth  power  of  1.12  ? 

6.  What  is  the  second  power  of  4.86  ? 

7.  What  is  the  fifth  power  of  4? 

8.  Find  the  third  power  of  .3  to  three  places. 

9.  What  is  the  third  power  of  -J-? 

10.  What  is  the  fifth  power  of  1.04? 

11.  Raise  1.05  to  the  sixth  power. 

12.  What  is  the  eighth  power  of  f  ? 

13.  What  is  the  second  power  of  4|? 
14-  Expand  the  expression  65. 

328 


INVOLUTION  329 

15.  What  is  the  second  power  of  5£? 

16.  What  part  of  83  is  26. 

17.  What  is  the  difference  between  5C  and  46? 

18.  Expand  35  X  24? 

19.  Express  with  a  single  index,  473  X  4?5  X  476. 

20.  How  many  acres  are  in  a  square  lot,  each  side  of  which 
is  135  rods? 

21.  What  is  the  sixth  power  of  .01? 

22.  What  is  the  fourth  power  of  .03  ? 

23.  What  is  the  fifth  power  of  1.05? 

24.  What  is  the  third  power  of  .001  ? 

25.  What  is  the  second  power  of  .0044? 

26.  Each  side  of  a  room  is  12  feet  long.     How  many  square 
yards  of  carpet  will  be  required  to  cover  the  floor  ? 

21.  A  box  in  cubical  form  is  6J  feet  long  on  any  inner  side. 
How  many  cubic  inches  will  it  contain  ? 

28.  From  2.1254  subtract  1TV3. 

29.  From  the  fifth  power  of  |  take  the  fourth  power  of  -J . 

EVOLUTION 

483.  A  Root  is  the  number  which  is  multiplied  by  itself  a 
given  number  of  times  to  produce  a  given  power. 

484.  Evolution  is  the  process  of  finding  or  extracting  the  root 
of  a  power.  Evolution  is  the  exact  reverse  of  Involution. 

485.  The  Radical  Sign  is  a  character  V  placed  over  the  num- 
ber considered  as  the  power  to  indicate  that  the  root  is  to  be  ex- 
tracted. 

486.  The  Index  of  the  root  is  a  small  figure  placed  above  the 
radical  sign  to  indicate  what  root  is  to  be  extracted.    Thus  <&  in- 
dicates that  the  third  or  cube  root  of  64  is  to  be  extracted.     The 
square  root  is  indicated  by  the  radical  sign  alone  without  any  in- 
dex. 

487.  A  Perfect  Power  is  a  number  whose  root  can  be  exactly 
extracted.    Thus  64  is  a    perfect  power  whose  third  or  cube  root 
is  4. 


330 


NEW    BUSINESS    ARITHMETIC 


488.  An  Improper  Power  is  a  number  whose  root  cannot  be 
exactly  extracted.    Thus  10  whose  square  root  is  3.1622-}-. 

The  only  roots  that  are  of  much  practical  use  are  the  Square 
and  Cube  roots. 

SQUARE  ROOT 

489.  The  Square  Root  of  a  number  is  one  of  the  two  equal 
factors  that  produce  the  number.    Thus  the  square  root  of  25  is  5. 

By  trial  and  inspection  we  find  that  the  square  of  any  number 
has  twice  as  many  or  one  less  than  twice  as  many  figures  as  the 
number.  Hence  the  square  root  of  a  number  will  contain  as  many 
figures  as  one-half  the  number  of  figures  in  the  power  and  one 
figure  more  for  an  odd  figure  in  the  power. 

1.  Find  the  square  root  of  576  sq.  ft. 


SOLUTION 

5'76|2£ 
4 


44 


176 
176 


20  rr 


20  FT 


EXPLANATION. — Pointing  off  the  power  into 
periods  of  two  places  each  by  the  principle 
just  laid  down  we  see  that  there  will  be  two 
figures  in  the  root.  Now  it  is  required  to  con- 
struct a  square  which  shall  contain  57G  sq. 
ft.  We  can  see  that  the  root  of  the  left  period 
is  2  and  since  there  will  be  two  figures  in  the 
root,  this  must  be  2  tens  or  20  ft.  Construct  a 
square  which  shall  be  20  feet  on  each  side  as 
in  the  diagram.  The  surface. of  this  square 
is  20  X  20  =  400  sq.  ft.  But  subtracting  this 
400  ft.  (expressed  as  4  in  hundreds  place  in 
the  solution)  we  still  have  176  sq.  ft.  Our 
square  must  be  increased  to  absorb  this  176 
sq.  ft.  This  can  be  done  by  adding  to  two 
sides,  and  still  retain  the  figure  as  a  square. 
These  two  additions  will  together  be  40  ft.  long, 
and  this  explains  why  we  "double  the  root  al- 
ready found,"  in  the  solution.  Now  the  length 
of  our  additions  being  40  ft.  the  width  will  be 
as  much  as  the  length  is  contained  times  in 
the  area.  176  +  40  =  4  ft.  and  this  gives  the 
second  figure  of  the  root.  But  our  square  is 
not  yet  complete.  We  still  require  a  corner 
which  we  find  is  4  ft.  square.  This  corner 
added  to  the  additions  on  the  two  sides  gives 
the  length  of  the  three  additions  as  44  ft. 


INVOLUTION 


331 


2O  FT 


and  thus  may  be  seen  why  we  add  the  last  fig- 
ure of  the  root  to  double  the  first.  44  ft.  being 
the  length  of  our  additions  and  4  ft.  being  their 
width,  multiplying  we  have  176  sq.  ft.  as  the 
area,  and  this  we  find  exactly  absorbs  the  re- 
maining area  given  in  the  power. 

We  have  therefore  constructed  a  square, 
each  side  of  which  is  24  feet  long,  and  the 
area  of  which  exactly  equals  the  area  given, 
therefore  we  conclude  that  24  feet,  the  length 
of  one  side  is  the  square  root  of  the  given  area, 
576  feet. 

From  this  solution  and  explanation  we  have  the  following: 

To  Find  the  Square  Root 

a.  Begin  at  the  right  hand  and  point  off  in   periods   of   two 
figures  each. 

b.  Find  the  greatest  square  in  the  left  hand  period  and  place  its 
root  in  the  quotient. 

c.  Subtract  the  square  from  the  left  hand  period  and  bring 
down  the  next  period. 

d.  Double  the  root  already  found  and  place  this  at  the  left  of 
the  dividend  for  a  trial  divisor.    Find  how  often  this  is  contained 
in  the  dividend,  exclusive  of  the  right  hand  figure,  and  place  the 
quotient  in  the  result  as  the  second  figure  of  the  root. 

e.  Annex  the  last  figure  of  the  root  to  the  trial  divisor  for  the 
complete  divisor.    Multiply  the  complete  divisor  by  the  last  figure 
of  the  root,  write  this  under  the  dividend,  subtract,  bring  dotvn 
the  next  period  if  any,  and  continue  as  before. 

NOTE. — The  square  root  of  a  fraction  consists  of  the  square  root 
of  its  numerator  over  the  square  root  of  its  denominator. 

Or,  the  fraction  may  be  reduced  to  a  decimal  and  then  the  root  ex- 
tracted 

2.  Find  the  square  root  of  1024. 

3.  Find  the  square  root  of  1849. 

4.  Find  the  square  root  of  4225. 

5.  Find  the  square  root  of  61504. 

6.  Find  the  square  root  of  444889. 


332  NEW    BUSINESS    ARITHMETIC 

7.  Find  the  square  root  of  390625. 

8.  Find  the  square  root  of  1679616. 

9.  Find  the  square  root  of  *?j. 

10.  Find  the  square  root  of  30 J. 

11.  Find  the  square  root  of  yVsV 

12.  Find  the  square  root  of  277?. 

13.  Find  the  square  root  of  J. 

14.  Find  the  square  root  of  3. 

15.  Extract  the  square  root  of  f . 

.  16.  Extract  the  square  root  of  17f. 

17.  Extract  the  square  root  of  .008836. 

18.  Extract  the  square  root  of  .00006561. 

19.  What  is  the  value  of  \/~3? 

20.  What  is  the  value  of  V  125? 

APPLICATIONS  OF  SQUARE  ROOT 

490.  An  Angle  is  the  space  included  between  two  straight 
lines  which  meet.     Thus  the  two  lines  B  A  and  C  A  meet  and 
form  an  angle  at  A. 

491.  A  Triangle  is  a  figure  bounded  by  three  straight  lines. 
The  accompanying  figure  is  a  triangle. 

492.  A  Right- Angle  is  the  space  between  two 
lines  when  one  is  perpendicular  to  the  other.    Thus 
the  angle  at  B  is  a  right-angle. 

493.  A    Right- Angled    Triangle    is    a    triangle 
having  in  it  a  right  angle. 

494.  The  Hypotenuse   is  the  longest   side,   or 
the  slanting  side.    Thus  A  C  is  the  hypotenuse. 


B  495.  The  Base  is  the  side  upon  which  the  tri- 

angle rests.    Thus  B  C  is  the  base. 

496.  The  Perpendicular  is  the  side  which  stands  at  right 
angles  with  the  base.    Thus  A  B  is  the  perpendicular. 


INVOLUTION  333 

It  is  a  known  principle,  discovered  and 
demonstrated  over  two  thousand  years 
ago  by  a  Greek  philosopher  and  mathe- 
matician that  the  area  of  the  square  de- 
scribed on  the  hypotenuse  of  a  right- 
angled  triangle  is  equal  to  the  sum  of  the 
areas  of  the  squares  described  on  the 
other  tivo  sides. 
From  this  principle  we  have  the  following: 

To  Find  the  Hypotenuse 

a.  Add  the  square  of  the  base  and  perpendicular  together  and 
extract  the  square  root. 

To  Find  Either  of  the  Shorter  Sides 

Subtract  the  square  of  the  given  side  from  the  square  of  the 
hypotenuse,  and  extract  the  square  root. 

1.  The  base  of  a  right-angled  triangle  is  30  ft.  and  the  per- 
pendicular is  40  ft.  What  is  the  hypotenuse? 

'   2.  The  base  of  a  right-angled  triangle  is  18  ft.  and  the  hypot- 
enuse is  22  ft.    What  is  the  perpendicular  ? 

3.  The  perpendicular  of  a  right-angled  triangle  is  64  inches 
and  the  hypotenuse  is  82  inches.  What  is  the  length  of  the  base? 

4-  A  church  steeple  is  128  ft.  high  and  stands  72  feet  from 
the  opposite  side  of  the  street.  What  is  the  length  of  a  rope  which 
will  reach  from  the  top  of  the  steeple  to  the  opposite  side  of  the 
street  ? 

5.  A  window  is  16  ft.  4  in.  from  the  ground.     What  length 
of  a  ladder  the  foot  of  which  placed  14  ft.  8  in.  from  the  house, 
will  reach  to  the  window  ? 

6.  A  square  field  contains  40  A.     How  many  rods  of  fence 
will  be  required  for  one  side  of  it?     How  many  rods  of  fence 
will  be  required  to  entirely  enclose  it? 

7.  A  city  lot  in  the  form  of  a  rectangle  contains  5650  sq.  ft. 
and  its  length  is  twice  its  width.    What  are  its  dimensions? 

S.  A  maypole  broke  off  23  ft.  from  the  ground  and  in  falling 
the  top  struck  the  ground  14  ft.  from  the  bottom  of  the  pole.  How 
high  was  the  pole? 


334 


NEW    BUSINESS    ARITHMETIC 


9.  A  park  is  one  mile  square.    What  is  the  length  ot  a  diag- 
onal path  across  it? 

10.  How  many  rods  of  travel  does  A  save  who  goes  diago- 
nally across  a  field  1  mile  square  in  preference  to  going  by  its  two 
sides  ? 

11.  A  room  is  30  feet  long,  25  feet  wide  and  12  feet  high. 
What  is  the  distance  from  one  of  the  lower  corners  of  the  room  to 
the  opposite  upper  corner? 

CUBE  ROOT 

497.  The  Cube  Root  of  a  number  is  one  of  three  equal  factors 
which  produce  the  number.  Thus  the  cube  root  of  64  is  4. 

By  trial  we  find  that  the  cube  of  any  number  consisting  of  one 
figure  can  never  exceed  three  figures,  the  cube  of  a  number  con- 
sisting of  two  figures  can  never  exceed  six  figures,  etc.  Hence 
if  we  point  off  the  power  into  periods  of  three  figures  each  the 
number  of  periods  will  indicate  the  number  of  figures  in  the  root. 
1.  Find  the  cube  root  of  91125  cu.  in. 


SOLUTION 

91'125|45 
64 


5425 


480027125 
600 
25 


27125 


E  X  P  L  A  N  A  TION. — 

Pointing  off  the  power 
into  periods  of  three 
places  each,  by  the 
principle  just  given, 
we  see  that  the  root 
will  contain  two 
places.  It  is  required 
to  construct  a  cube 
which  shall  contain 
91125  cu.  in.  We 

see  by  inspection  that  the  cube  root  of  the  left 
period  is  4  and  since  there  are  to  be  two  figures 
in  the  root  this  is  4  tens  or  40.  Construct  a 
cube  which  shall  be  40  in.  on  each  side  as  in 
the  diagram.  The  solid  contents  of  this  cube 
is  40  x  40  X  40  =  64000  cu.  in.  But  subtract- 
ing the  64000  cu.  in.  (expressed  in  the  solu- 
tion as  64  in  thousands  place)  we  still  have 
27125  cu.  in.  left.  Our  cube  must  be  increased 
so  as  to  absorb  this,  which  can  be  done  by 
adding  to  three  sides  of  the  cube,  and  still  re- 


INVOLUTION 


335 


tain  its  cubical  form.  The  surface  of  one 
face  of  the  cube  contains  40  X  40  =  1600  sq. 
in.  and  3  faces  will  contain  3  times  1600  sq. 
in.  or  4800  sq.  in.  This  explains  why  we 
"square  the  root  found  and  multiply  it  by  300 
for  a  trial  divisor,"  300  being  used  instead  of 
3  because  we  have  used  the  root  found  as 
units  when  they  are  really  tens.  We  find  that 
our  trial  divisor  is  contained  in  the  dividend 
5  times  and  this  gives  us  the  thickness  of  the 
additions.  But  our  cube  is  not  yet  perfect.  We 
must  add  three  rectangular  pieces  at  the  cor- 
ners. These  pieces  will  be  40  in.  long  and  5  in. 
wide  and  there  being  three  of  them  their  sur- 
face will  be  40  X  5  X  3  =  600  sq.  in.  This  ex- 
plains why  we  "multiply  the  last  figure  of  the 
root  by  the  last  and  by  30;"  30  being  used  in- 
stead of  3  because  we  called  the  40  four  units 
instead  of  4  tens,  which  they  really  are.  But 
our  cube  is  still  imperfect.  We  must  add  a 
small  block  at  the  corner.  This  will  be  5  in. 
long  and  5  in.  wide  and  hence  its  surface  will 
be  5  X  5  =  25  sq.  in.  which  is  also  written  in 
the  divisor.  Our  complete  divisor  then  is 
5425  sq.  in.  which  is  the  surface  of  all  of  the 
additions  that  we  have  made.  Now  multiply- 
ing this  by  the  thickness,  5  in.,  we  have  the 
solid  contents  of  all  of  these  additions,  27125 
cu.  in.  and  this,  we  find,  exactly  consumes  the 
cubical  contents  given. 


From  this  solution  and  explanation  we  have  the  following : 


To  Find  the  Cube  Root 

a.  Begin  at  the  right  hand  and  point  off  in  periods  of  three 
places  each. 

b.  Find  the  greatest  cube  in  the  left  hand  period  and  place  its 
root  in  the  quotient. 

c.  Subtract  the  cube  from  the  left  hand  period  and  bring  down 
the  next  period. 


336  NEW   BUSINESS  ARITHMETIC 

d.  Square  the  root  found  and  multiply  it  by  3  for  a  trial  di- 
visor and  affix  or  add  two  ciphers.     Find  how  often  this  is  con- 
tained in  the  dividend  and  place  the  quotient  in  the  result  as  the 
next  -figure  of  the  root. 

e.  Multiply  the  last  figure  of  the  root  by  the  rest  and  by  3  and 
add  or  affix  one  cipher,  and  write  the  result  under  the  trial  divisor. 

f.  Square  the  last  figure  of  the  root  and  place  the  result  under 
the  trial  divisor. 

g.  Add  together  the  trial  divisor  and  the  two  quantities  beneath 
it  and  this  will  be  the  complete  divisor  which  multiply  by  the  last 
figure  of  the  root.     Write  the  product  under  the  dividend,  sub- 
tract,  bring  down  the  next  period ',  if  any,  and  continue  as  before. 

2.  Find  the  cube  root  of  46656. 

3.  Find  the  cube  root  of  250047. 
4-  Find  the  cube  root  of  2000376. 

5.  Find  the  cube  root  of  5545233. 

6.  Find  the  cube  root  of  10077696. 

7.  Find  the  cube  root  of  46268279. 

8.  Find  the  cube  root  of  85766121. 

9.  Find  the  cube  root  of  153990656. 

10.  Find  the  cube  root  of  250047000. 

11.  What  is  the  cube  root  of  926.859375? 

12.  What  is  the  cube  root  of  44.6  ?  » 

Extract  the  cube  root  of  the  following  numbers: 


13.     ^  1  16.     V  9 


14.  ^  2  17.     V  13. 

15.  y~3~  18.     &~W 

APPLICATIONS  OF  CUBE  ROOT 

1.     What  is  each  side  of  a  square  box,  the  solid  contents  of 
is  59319  cu.  inches? 


INVOLUTION  337 

6.  What  is  the  length  of  each  side  of  a  cubic  vessel  whose 
solid  contents  is  2936.493568  feet? 

3.  A  store  has  its  length,  breadth  and  height  all  equal ;  it  can 
hold  185193  cubic  feet  of  goods;  what  is  each  dimension? 

4.  How  many  linear  inches  must  each  dimension  of  a  cubic 
vessel  be  which  can  hold  997002999  cubic  inches  of  water? 

5.  What  will  be  the  length  and  depth  of  a  bin  which  shall 
contain  160  bushels  of  corn,  if  its  length  is  twice  its  width,  and 
its  depth  and  width  are  equal  ? 

G.  A  bin  is  18  ft.  long',  12  ft.  wide  and  10  ft.  deep.  What 
must  be  the  length  of  a  cubical  bin  having  the  same  volume  ? 

7.  Give  the  dimensions  of  a  cube  having  the  same  volume  as 
a  box  5  ft.  4  in.  long,  2  ft.  8  in.  wide  and  3  ft.  6  in.  deep. 

S,  What  is  the  surface  of  the  six  faces  of  a  cube  containing 
91125  cubic  feet? 

9.  A  cistern  in  the  form  of  a  cube  holds  150  barrels  of  water. 
What  is  each  of  its  dimensions  ? 

10.  A  cubical  bin  holds  350  bushels  of  wheat.     What  is  its 
length  ? 

11.  Find  the  length  of  a  cubical  cistern  which  holds  5000 
gallons  of  water. 


22 


MENSURATION 

498.  Mensuration  is  the  art  of  computing  lengths,  surfaces 
and  volumes. 

499.  A  Line  is  that  which  has  length  only.    All  lines  in  men- 
suration and  surveying  are  imaginary. 

500.  A  Straight  Line  is  the  shortest  distance  between  two 
points. 

501.  A  Curved  Line  is  a  line  having  no  part  straight. 

502.  A  Horizontal  Line  is  a  line  parallel  with  the  horizon,  or 
with  the  water  level. 

503.  A  Vertical  Line  is  a  line  perpendicular  to  the  horizon. 

504.  An  Angle  is  the  space   between   two 
lines  which  meet. 


Thus  the  space  between  the  lines  A  C  and  B  C 
is  an  angle,  called  the  angle  A  C  B. 

505.  A  Right  Angle  is  an  angle  formed  by  the 
meeting  of  a  horizontal  line  and    a    perpendicular 


angle. 


Right 
angle. 


An  obtuse  angle  is  one  which  is  greater  than  a  right 
angle.     An  acute  angle  is  one  which  is  less  than  a 
right  angle. 

__  ._  _,        .  1  .    <       1  1  Obtuse        /    Acute 

506.  A  Surface  is  that  which   has    length       angle.     /    angle. 
and  breadth.  B 


A  Plane  is  a  surface  such  that  any  two  points  of  it  can  be  joined  by  a 
straight  line,  which  lies  wholly  in  the  surface.  The  application  of  a 
straight  line  is  the  test  of  a  plane. 

507.  Area  is  a  term  applied  to  the  quantity  of  surface  con- 
tained in  a  figure  having  only  length  and  breadth. 

338 


MENSURATION 


339 


508.  A  Solid  is  that  which  has  length,  breadth  and  thickness. 
PLANE  FIGURES 


509.  To  find  the  area  of  a  square  or  rectangle. 

510.  A  Square  is  a  figure  having  four  equal 
sides. 


A   SQUARE. 


511.  A  Rectangle  is  a  figure  having  four 
right  angles  and  its  opposite  sides  equal. 

The  reason  for  the  following  rule  will  be  found 
by  referring  to  Art.  172. 


A    RECTANGLE. 


Rule.     Multiply  the  length  by  the  breadth,  and  the  product 
will  be  the  surface  or  area. 

PROBLEMS 

1.  What  will  it  cost  to  pave  a  sidewalk  80  ft.  long  and  15  ft. 
wide  at  $1.50  per  sq.  yard? 

2.  How  much  will  a  farm  cost  which  is  185  rods  long  and  125 
rods  wide  at  $45  per  acre  ? 

3.  How  many  small  squares  each  containing  4  square  inches, 
are  contained  in  a  large  one  which  is  4  feet  square  ? 

4.  What  will  it  cost  to  plaster  a  room  15  ft.  6  in.  long  12  ft. 
9  in.  wide  and  10  ft.  3  in.  high  at  37-J-  cents  per  square  yard? 

').  How  many  yards  of  carpeting  f  yd.  wide  will  cover  a  floor 
16  ft.  9  in.  long  by  15  ft.  9  in.  wide,  if  laid  lengthwise? 

512.  To  find  the  area  of  a  triangle. 

513.  The  Base  of  a  triangle  is  the  side  on  which  it  rests. 

514.  The  Altitude  of  a   triangle   is  the   perpen- 
dicular distance  from  the  base  to  the   opposite    angle 
called  the  apex. 


Since  every  angle  in  equivalent  to  one-half  of  a  square 
or  parallelogram  having  the  same  base,  we  may  find  the  area 
of  the  squares  or  parallelogram  and  divide  by  two,  or  3/*-cording  to  the 
following: 


340  NEW    BUSINESS    ARITHMETIC 

Rule.  Multiply  the  base  of  the  triangle  by  its  height,  and  di- 
vide the  result  by  two. 

PROBLEMS 

1.  How  many  square  yards  in  a  triangle  whose    base    is    27 
yards  and  altitude  36  yards? 

2.  The  gable  end  of  a  house  was  34  ft.  6  in.  from  eave  to 
eave  and  the  perpendicular  height  of  the  ridge  above  the  eaves 
is  -13  ft.    How  many  feet  of  boards  will  be  required  to  cover  three 
such  gables  ? 

3.  A  lot  of  ground  80  ft.  long  by  20  ft.  wide  was  cut  diago- 
nally by  a  railroad,  leaving  a  triangular  plot  of  the  same  base  and 
altitude ;  what  was  its  area  ? 

4.  What  is  the  rent  of  a  triangular  field  whose  base  is  80  rods 
and  perpendicular  height  48  rods,  at  $4.50  per  acre? 

515.  To  find  the  circumference  or  diameter  of  a  circle. 

516.  A  Circle  is  a  plane  figure  bounded  by  a  curve  line,  every 
part  of  which  is  equally  distant  from  a  point  within  called  the 
center. 

517.  The  Circumference  of  a  circle  is  the  curved  line  by  which 
it  is  bounded. 

518.  The  Diameter  is  a  straight  line  drawn  through  the  center, 
terminating  at  each  end  in  the  circumference. 

519.  The  Radius  is  a  straight  line  drawn  from  the  center  to 
the  circumference,  and  is  equal  to  half  the  diameter. 

It  has  been  proven  in  geometry  that  the  circumference  of  every  circle 
great  or  small  is  3.1416  times  its  diameter,  hence  the 

Rule.  a.  To  find  the  circumference  of  a  circle  multiply  the 
diameter  by  3.1416. 

b.  To  find  the  diameter  of  a  circle  divide  the  circumference  by 
3.1416. 

PROBLEMS 

1.  What  is  the  diameter  of  a  circular  piece  of  land  measur- 
ing 5  J  miles  around  it  ? 


MENSURATION  341 

2.  The  diameter  of  a  circular  race  course  is  f  of  a  mile,  how 
many  rods  of  fence  will  be  required  to  enclose  it? 

3.  A  circular  park  is  two  miles  in  circumference;  what  is  its 
diameter  ? 

4.  A  horse  is  fastened  to  a  tree  by  a  rope  37£  feet  long.    What 
is  the  circumference  of  the  circle  in  which  he  may  graze  ? 

5.  What  is  the  diameter  of  a  wheel  which  makes  420  revolu- 
tions in  a  minute  when  the  cars  are  running  at  the  rate  of  45  miles 
per  hour  ? 

520.  To  find  the  area  of  a  circle. 

Rule.    Multiply  the  diameter  by  the  circumference  and  divide 
the  product  by  4-     Or,  multiply  the  square  of  the  diameter  by 

.7854. 

PROBLEMS 

1.  What  is  the  area  of  a  circle  whose  diameter  is  36  feet? 

2.  A  circular  park  requires  145  rods  of  fence  to  enclose  it, 
how  many  acres  does  it  contain? 

3.  Find  the  area  of  a  space  on  which  a  horse  may  graze  when 
confined  by  a  rope  125  feet  long. 

4.  A  circular  fish  pond  has  a  radius  of  75  feet;  what  is  its 
area? 

5.  How  many  square  feet  in  a  circular  grass  plot  75    feet   in 
diameter  ? 

SOLIDS 

521.  A   Solid   is   that   which   has   length, 
breadth  and  thickness. 

522.  A  Prism  is  a  solid  whose  bases  are 
similar,   equal   and   parallel,   and   whose   sides 
are  parallelograms. 

523.  All  rectangular  solids  are  prisms. 

524.  A  Right  Prism  is  one  whose  sides  are 
perpendicular  to  its  bases. 


342 


NEW     BUSINESS     ARITHMETIC 


525.  A   Rectangular  Prism  is  one   whose 
bases  are  rectangular  and  its  sides  perpendicu- 
lar to  its  bases. 

526.  A    Triangular   Prism    is    one    whose 
bases  are  triangles. 

NOTES. — 1.     Prisms  are  named  from  the  form 
of  their  bases,  as  triangular,  quadrangular,  pentag- 
onal, hexagonal,  etc. 

2.     When  their  sides  are  all  equal  to  each  other 
they  are  called  cubes. 

527.  A  Cylinder  is  a  round  prism,  or  one  hav- 
ing circles  for  its  ends. 

528.  A  Pyramid  is  a  solid  having  for  its  base 
any  plane  figure  and  for  its  sides  triangles  which 
terminate  in  a  common  point  called  the  vertex. 

529.  A  Cone  is  a  body  which  has   a   circle   for 
a  base  and  whose  sides  terminate  in  a  point  called 
the  vertex. 

530.  A  Frustum  of  a  pyramid   or   cone   is   the 
part  which  is  left  after  the  top  is  cut  off  by  a  plane 
parallel  or  inclined  to  the  base. 

531.  To  find  the  surface  of  a  prism  or  any  figure  having  plain 
sides. 

Rule.    Find  the  area  of  each  surface  separately,  and  add  the  re- 
sults. 

PROBLEMS 

1.  Each  side  of  a  triangular  prism  is  3  ft.  long  and  9  inches 
wide.    What  is  the  area  of  its  surface,  not  including  the  ends  ? 

2.  What  is  the  area  of  a  pyramid  having  6  sides  each  2  feet 
at  base  by  6  feet  in  slant  height  ? 

532.  To  find  the  convex  surface  of  a  cylinder. 

Rule.    Multiply  the  circumference  of  the  base  by  the  altitude. 

PROBLEMS 

1.  How  many  square  feet  of  surface  in  the  sides  of  a  cylinder 
16 J  feet  long  and  12  feet  in  circumference? 


MENSURATION  343 

2.  A  smoke  stack  is  40  feet  high  and  9  feet  4  inches  in  cir- 
cumference.    How  many  square  feet  of  sheet  iron  are  contained 
in  it? 

3.  What  is  the  surface  including  the  ends,  of  a  cylinder  5  feet 
long  and  H  feet  in  diameter? 

4-  A  log  is  60  ft.  long  and  10  ft.  in  circumference.  What  is 
the  surface  of  its  sides? 

533.  To  find  the  solid  contents  of  a  prism  or  cylinder. 
Rule.    Multiply  the  area  of  the  base  by  the  altitude. 

PROBLEMS 

1.  Find  the  solid  contents  of  a  square  prism,  the  base  being  5 
feet  each  side,  and  17  feet  high. 

2.  A  well  is  45  feet  deep  and  4  feet  in  diameter.    How  many 
gallons  of  water  will  it  hold? 

3.  A  cistern  is  8  feet  by  6  feet  and  14  feet  deep.    What  is  its 
solid  contents  in  gallons? 

534.  To  find  the  solid  contents  of  a  pyramid  or  a  cone. 

It  has  been  demonstrated  in  geometry  that  a  pyramid  is  l/z  of  a  prism 
of  the  same  base  and  height  and  a  cone  is  y$  of  a  cylinder  of  the  same 
base  and  height. 

Rule.  Multiply  the  area  of  the  base  by  the  altitude  and  divide 
by  3. 

PROBLEMS 

1.  What  are  the  contents  of  a  pyramid  whose  base  contains 
144  square  feet  and  its  altitude  is  36  feet? 

2.  What  are  the  contents  of  a  cone  whose  base  contains  3624 
square  feet  and  its  altitude  is  27  feet? 

3.  A  monument  in  the  form  of  a  pyramid  is  18  ft.  6  in.  by  16 
ft.  9  in.  at  the  base,  and  its  altitude  is  67  ft.  3  in.     What  is  the 
amount  of  solid  stone  contained  in  it? 

4-  A  pyramid  is  430  ft.  high  and  each  side  of  its  base  is  520 
feet.  What  are  its  solid  contents? 

535.  To  find  the  surface  of  a  globe,  the  circumference  and 
diameter  being  given. 


344  NEW    BUSINESS    ARITHMETIC 

536.  A  Globe  or  sphere  is  a  body  every  point  of  the  surface 
of  which  is  equally  distant  from  a  point  within  called  the  center. 

537.  The  Diameter  of  a  sphere  is  a  straight  line   passing 
through  the  center  and  terminating  both  ways  at  the  circumfer- 
ence. 

538.  A  Hemisphere  is  half  a  sphere. 

Rule.   .  Multiply  the  square  of  the  diameter  by  3.1416. 

PROBLEMS 

1.  A  perfect  sphere  is  34  feet  in  diameter.     What  is  its  sur- 
face? 

2.  What  will  it  cost  to  gild  a  ball  12  inches  in  diameter  at  10 
cents  a  square  inch? 

3.  If  the  earth  is  7912  miles  in  diameter  what  is  its  area,  sup- 
posing it  to  be  a  perfect  sphere  ? 

539.  To  find  the  solid  contents  of  a  sphere. 
Rule.     Multiply  the  cube  of  the  diameter  by  .5236. 

PROBLEMS 

1.  What  is  the  solid  contents  of  a  cannon  ball  15  inches  in 
diameter  ? 

2.  A  balloon  is  30  ft.  in  diameter.     How  many  cubic  feet  of 
gas  does  it  contain,  supposing  it  to  be  a  perfect  sphere? 

3.  The  basin  of  a  fountain  is  a  hemisphere  22^  ft.  in  diameter ; 
what  are  its  cubical  contents? 

4.  How  many  hogsheads  of  water  will  it  contain? 


METRIC  SYSTEM 

540.  The  Metric  System  of  weights  and  measures  is  a  system 
in  which  the  denominations  increase  and  decrease  by  the  decimal 
scale. 

The  metric  system  originated  in  France,  and  on  account  of  its  sim- 
plicity has  been  adopted  in  nearly  all  European  countries,  Mexico,  South 
America,  and  in  1866  by  the  Congress  of  the  United  States.  Its  use  in 
the  United  States  has  not  become  general,  but  is  confined  mostly  to  the 
arts  and  sciences,  the  coast  survey  and  a  portion  of  the  mint  and  post 
office.  For  this  reason  the  subject  will  not  be  extensively  treated  in  this 
book. 

541.  The  Meter  is  the  base  of  the  system  and  is  one  ten 
millionth  part  of  the  distance  from  the  equator  to  the  pole,  or 
39.37  inches,  nearly. 

The  Metric  System  has  three  principal  units,  the  Me'ter 
(meeter),  Li'ter  (leeter)  and  Gram.  To  these  are  added  the  Ar 
and  Ster  for  square  and  cubic  measure.  Each  of  these  units  has 
its  multiples  and  divisions. 

542.  The  Lower  Denominations  are  formed  by  prefixing  to 
the  name  of  the  unit,  dec'i,  cen'ti  and  mil'li. 

Thus  from  dec1 i,  yV  we  have  dec'i  me'ter  yV  meter. 

from  cen  ti,  T^¥  we  have  cen'ti  me'ter  TOIT  meter, 
from  mil'li,  -nnnr  we  have  mil'li  me'ter  nAnr  meter. 

543.  The  Higher  Denominations  are  formed  by  prefixing  to 
the  name  of  the  unit,  dek'a,  hek'to,  kil'o  and  myr'ia. 

Thus  from  dek' a,  10  we  have  dek'a  me'ter  10  meters. 

from  hek'  to,  100  we  have  hek'to  me'ter  100  meters, 
from  kil'o,  1000  we  have  kil'o  me'ter  1000  meters, 
from  myr '  ia,  10000  we  have  myr '  ia  me '  ter  10000  meters. 

345 


346  NEW   BUSINESS   ARITHMETIC 

Metric  Linear  Measure 

TABLE 

10  mil'li-me'ters  (mm.)     =  1  Cen'ti-me'ter cm.  (^  m.) 

10  cen'ti-me'ters  =  1  dec'i-me'ter dm.  (^  m.) 

10  dec'i-me'ters  =  1  METER m. 

10  me'ters  =  1  dek'a-me'ter Dm.   (10  m.  ) 

10  dek'a-me'ters  =  1  hek'to-me'ter Hm.  (100  m.) 

10  hek'to-me'ters  =  1  Kil'o-me'ter Km.  (1000  m.) 

10  kil'o-me'ters  =  1  myr'ia-me'ter Mm.   (10000  m.) 

NOTES. — 1.  The  principal  unit  of  each  table  is  printed  in  capital  let- 
ters ;  those  in  common  use  in  full-faced  Roman. 

2.  The  Accent  of  each  unit  and  prefix  is  on  the  first  syllable,  and 
remains  so  in  the  compound  words. 

3.  Abbreviations  of  the  higher  denominations  begin  with  a  capital, 
those  of  the  lower  with  a  small  letter. 

Metric  Square  Measure 

TABLE 

100  square  centimeters,  sq.  cm.  =  1  square  decimeter  =  15.5  -f  sq.  in. 
100  square  decimeters,  sq.  dm.  =  1  square  meter  =  1.196  sq.  yd. 

NOTE. — It  will  be  observed  that  the  units  of  square  measure  are  the 
squares  of  the  units  of  linear  measure.  Therefore  100  units  of  any  de- 
nomination are  the  equivalent  of  1  unit  of  the  next  higher  denomination. 

Metric  Land  Measure 

TABLE 

1  centare,  ca.  =  1  sq.  M. 
100  centare  =  1  are,  A. 
100  A  =1  hectare. 

NOTE. — The  hectare  is  the  unit  used  in  the  measurement  of  land  as 
the  acre  is  the  common  unit  in  this  country.  It  is  the  equivalent  of  10,000 
square  meters. 

Metric  Cubic  Measure 

TABLE 

1000  cu.  millimeters,  cu.  mm.  =  1  cu.  centimeter. 
1000  cu.  centimeters,  cu.  cm.  =  1  cu.  decimeter. 
1000  cu.  decimeters,  cu.  dm.  =  1  cu.  meter. 

NOTE. — It  will  be  observed  that  the  units  of  cubic  measure  are  the 
cubes  of  the  units  of  linear  measure.  Therefore  1000  units  of  any  de- 
nomination are  the  equivalent  of  1  unit  of  the  next  higher  denomination. 


METRIC   SYSTEM 


347 


Metric  Wood  Measure 

TABLE 

10  decisters,  ds.  =  1  ster. 

10  sters,  s.  =1  dekaster. 

NOTE. — In  wood  measure  the  ster  is  the  unit.  It  is  the  equivalent 
of  one  cubic  meter. 

Metric  Measure  of  Capacity 

TABLE 

1  milliliter,  ml.  =  ujfoj  of  a  liter. 

10  milliliters         =  1  centiliter,  cl. 

10  cl.  =  1  deciliter,  dl. 

10  dl.  =  1  liter,  1. 

10  1.  =1  dekaliter,  Dl. 

10  Dl.  =  1  hectoliter,  HI. 

10  HI.  =  1  kiloliter,  Kl. 

NOTE. — There  is  but  the  one  table  for  both  dry  and  liquid  measure 
and  the  unit  is  the  liter.  The  liter  is  the  equivalent  of  a  cubic  decimeter, 
1.0567  wine  quarts  or  .908  dry  quarts. 

Measure  of  Weight 


TABLE 

f  gram  =  1.543  gram 
gram,  g. 
dekagram,  Dg. 
hectogram,  Hg. 
kilogram,  Kg.  or  Kilo, 
myriagram,  Mg. 
quintal,  Q. 
ton. 

In  the  metric  system  there  is  but  one  table  of  weight,  all  articles  both 
heavy  and  light  being  measured  by  it. 


1  decigram,  dg.  = 
10  dg. 
10  g. 
10  Dg. 
10  Hg. 
10  Kg. 
10  Mg. 
10  Q. 


Tables  of  Equivalents 


1  inch  =  2.54  centimeters. 
1  foot  =  .3048  of  a  meter. 
1  yard  =  .9144  of  a  meter. 
1  rod  =  5.029  meters. 
1  mile  =  1.6093  kilometers. 


LINEAR  MEASURE 

centimeter  =  .3937  of  an  inch, 
decimeter  =  .328  of  a  foot, 
meter  =  1.0936  yards, 
dekameter  =  1.9884  rods, 
kilometer  =  .62137  of  a  mile. 


348  NEW    BUSINESS    ARITHMETIC 

SQUARE  MEASURE 

1  sq.  inch  =  6.452  sq.  centimeters.  1  sq.  centimeter  =  .155  of  a  sq.  inch. 

1  sq.  foot  =  .0929  of  a  sq.  meter.  1  sq.  decimeter  =  .1076  of  a  sq.  foot 

1  sq.  yard  =  .8361  of  a  sq.  meter.  1  sq.  meter  =  1.196  square  yards. 

1  sq.  rod  =  25.293  of  a  sq.  meter.  1  are  =  3.954  sq.  rods. 

1  acre  =  40.47  ares.  1  hectare  =  2.471  acres. 

1  sq.  mile  _  259  hectares.  1  sq.  kilometer  =  .3861  of  a  sq.  mile. 

CUBIC   MEASURE 

1  cu.  inch  =  16.387  cu.  centimeters.  1  cu.  centimeter  —  .061  of  a  cu.  inch. 

1  cu.  foot  =  28.317  cu.  decimeter.  1  cu.  decimeter  =  .0353  of  a  cu.  ft. 

1  cu.  yard  =  .7645  of  a  cu.  meter.  1  cu.  meter  =  1.308  cu.  yard. 

1  cord  =  3.624  ster.  1  ster  =  .2759  of  a  cord. 

MEASURES  OF  CAPACITY 

1  liquid  quart  =  .9463  of  a  liter.  1  liter  =  1.0567  liquid  quarts. 

1  dry  quart  =  1.101  liter.  1  liter  =  .908  of  a  dry  quart. 

1  liquid  gallon  =  .3785  of  a  dekaliter.  1  dekaliter  =  2.6417  liquid  gallons. 

1  peck  =  .881  of  a  dekaliter.  1  dekaliter  -  1.135  pecks. 

1  bushel  =  .2524  of  a  hektoliter.  1  hektoliter  =  2.8375  bushels. 

MEASURES  OF  WEIGHT 

1  grain,  Troy  =  .0648  of  a  gram.  1  gram  =  .03527  of  an  ounce,  Avoir. 

1  ounce,  Avoir.  =  28.35  gram.  1  gram  =  .03215  of  an  ounce,  Troy. 

1  ounce,  Troy  =  31.104  grams.  1  gram  =  15.432  grains,  Troy. 

1  Ib.  Avoir.  =  .4536  of  a  kilogram.  1  kilogram  —  2.2046  pounds,  Avoir. 

1  Ib.  Troy  =  .3732  of  a  kilogram.  1  kilogram  =  2.679  pounds,  Troy. 

1  ton  (short)  =  .9072  of  a  tonneau.  1  tonneau  =  1.1023  tons  (short). 

PROBLEMS 

1.  Reduce  763217  meters  to  kilometers. 

2.  Reduce  318.462  kilometers  to  meters. 

S.  Reduce  395.16  kilometers  to  centimeters. 

4.  Reduce  51626  centimeters  to  meters ;  to  kilometers. 

5.  If  a  man  traveled  171  kilometers  in  a  day,  how  many  miles 
did  he  travel  ? 

6.  If  it  cost  $.22J  per  meter  for  a  fence,  what  will  be  the  cost 
of  a  similar  fence  f  kilometers  long? 

7.  If  it  is  980  miles  from  New  York  to  Chicago,  how  many 
kilometers  is  it ;  how  many  hectometers  ? 

8.  18.5  yards  are  how  many  meters  ? 

9.  Write  6  meters,  3  decimeters  and  5  centimeters  as  one 
number  with  the  meter  as  the  unit. 


METRIC    SYSTEM  349 

10.  Express  19.763  m.  in  decimeters ;  in  centimeters. 

11.  In  5638  square  meters  how  many  ares;  how  many  hectares? 

12.  In  218.75  hectares  how  many  square  meters;  how  many 
centares? 

13.  How  many  hectares  in  a  farm  2.168  Km.  long  and  1.33 
Km.  wide? 

14-  What  is  the  cost  of  a  cement  walk  5.64  m.  long  and  f  m. 
wide  at  $2.60  per  sq.  m.? 

15.  A  farm  contains  192  hectares,  if  it  is  .376  Km.  wide  how 
long  is  it? 

16.  Express  in  hectares  the  equivalent  of  247.1  acres. 

17.  Write  as  cubic  meters  15  cubic  decimeters,  4  cubic  centi- 
meters and  8  cubic  millimeters. 

18.  Write   the   equivalent   of   these   numbers   in  cubic  deci- 
meters:  14  cu.  m.,  18  cu.  dm.,  36  cu.  cm. 

19.  A  vessel  is  1  m.  long,  f  m.  wide  and  1J  m.  high ;  how  many 
liters  does  it  contain  ? 

20.  If  a  gallon  of  milk  costs  $.25  what  should  be  the  price  per 
liter? 

21.  A  bin  contains  5689.35  hectoliters  of  wheat.     What  is  it 
worth  at  $.32  per  dekaliter?, 

22.  A  cistern  2.75  m.  by  3.25  m.  by  7.5  m.  will  hold  how 
many  dekaliters  ?    How  many  cu.  m.  ? 

23.  Write  as  liters  in  one  number  3  L,  6  dl.,  4  cl.  and  5  ml. 
2Jf.  How  many  grams  in  1  Kilo.  ? 

25.  How  many  kilograms  in  1  ton? 

26.  5  Kilos,  equal  how  many  pounds? 

27.  1  ton  equals  how  many  pounds  av.  ? 

28.  How  many  powders  of  7  grams  each  can  be  made  from 
637  kilograms? 

29.  How  many  sters  in  a  pile  of  wood  1  m.  wide,  3  m.  long  and 
j  m.  high  ? 

30.  How  many  cubic  meters  in  a  box  f  m.  wide,  1  j  m.  high  and 
3  m.  long? 

31.  In  46328  cu.  dm.  how  many  cu.  meters? 

82.  In  68.4  ares  there  are  how  many  square  meters? 


350 


NEW    BUSINESS    ARITHMETIC 


VALUES   OF   FOREIGN   COINS  IN  UNITED  STATES  MONEY 

(Proclaimed  by  the  Secretary  of  the  Treasury,  October  1,  1903) 


COUNTRY. 

Stand. 

Monetary  unit. 

•So!,; 

§S*J5 

|l«:i 
>~£ 

Coins. 

Argentine  Rep. 

Aust.-Hungary 

Belgium  . 
Bolivia  
Brazil  

British  Posses. 
N.  A.    (except 
Newf'nd)  
Cen.   Am.  St.— 
Costa  Rica.... 

Brit  Honduras 
Guatemala..  "] 
Honduras...  1 
Nicaragua  .  .  f 
Salvador....  j 
Chile  

China  

Gold  

Gold  

Gold... 
Silver.... 
Gold  

Gold  

Gold  
Gold  

Silver  . 

Peso- 
Crown 

Franc. 
Boliviz 
Milreif 

Dollar 

Colon.. 
Dollar 

Peso..  . 

mo  

$0.965 

.203 

.193 
.408 
.546 

1.000 

.465 
1.000 

.408 
.365 

.659 
.657 
.630 
.644 
.610 
.671 

.617 
(t) 
.652 
.618 
.634 
.643 
.602 
.609 
.663 
.639 
.408 
.926 

.268 
.487 

4.943 

.193 
.193 

.238 
4.866^ 

.193 
.965 

4.866^ 

.193 
.498 

1.000 
.443 

Gold:  argentine  ($4.824)  and  %  argtii- 
tine.    Silver:  peso  and  divisions. 
Gold:      former      system—  4    florins 
($1.929),    8  florins    ($3.858\     ducat 
($2.287)  and  4  ducats  ($9.  149).  Silver: 
1  and  2  florins. 
Gold:    present   system—  20    crowns 
($4.052);     10  crowns  ($2.026). 
Gold:  10  and  20  francs.  Silver:  5  francs. 
Silver:  boliviano  and  divisions. 
Gold:  5,  10  and  20  milreis.    Silver:    X, 
1,  and  2milreis. 

Gold:  2,  5,  10  and  20  colons   ($9.307). 
Silver:  5,  10,  25  and  50  centimes. 

Silver:  peso  and  divisions. 

Gold:  escudo  ($1.825),  doubloon  ($3.650\ 
and  condor  ($7.300).  Silver:  peso  and 
divisions. 

[dor.    Silver:  peso. 
Gold:  condor  ($9.647)  and  double-con  - 
Gold:    Doubloon   Isabella,     cent  en 
($5.017).    Alphonse    ($4.823).    Silver: 
peso. 
Gold:  10  and  20  crowns. 
Gold:    10    sucres     ($4.8665).      Silver: 
sucre  and  divisions. 
Gold:  pound  (100  piasters),  5,  10,  20  and 
50  piasters.    Silver:    1,  2,  5,  10  and  20 
piasters.                                      [($1.93). 
Gold:    20    marks     ($3.859),    10   marks 
Gold:    5,   10,  20,   50    and    100  francs. 
Silver:  5  francs. 
Gold:  5,  10  and  20  marks. 
Gold:  sovereign  (pound  sterling)  and 
^  sovereign.       [Silver:  5  drachmas. 
Gold:  5,   10,  20,  50  and  100  drachmas. 
Gold:  1,  2,  5  and  10  gourdes.    Silver: 
gourde  and  divisions. 
Gold:    sovereign     (pound     sterling.) 
Silver:  rupee  and  divisions.     [5  lire. 
Gold:  5,  10,  20,  50  and  100  lire.    Silver: 
Gold:  5,  10  and  20  yen.    Silver:   10,20 
and  50  sen. 

Gold:  dollar  ($0.983),  2&,  5,  10  and  20 
dollars.  Silver:  dollar  (orpeso>  and 
divisions. 

Gold  
Silver.... 

Peso... 
Tael..  <i 

'  Amoy  
Canton  
Chef  oo  
Chin  Kiang. 
Fuchau  .... 
Haikwan 
(Customs.) 
Hankow.... 
Hongkong.. 
Nanking.... 
Niuchwang 
Ningpo  .... 
Peking  
Shanghai  .  . 
Swatow  — 
Takau  
.  Tientsin  .  .  . 

Colombia  
Cuba  

Denmark  
Ecuador  

Egypt  

Finland  
France  

German  Emp.  . 
Great  Britain.. 

Greece  
Haiti  

India  

Silver.... 
Gold  

Gold  
Gold  

Gold  

Gold.... 
Gold  

Gold... 

Peso... 
Peso... 

Crown 
Sucre  . 

Pound 

Mark.  . 
Franc. 

Mark.. 

(100  piasters) 

Gold  

Gold  
Gold  

Gold  

Pound 

Drachi 
Gourd< 

Pound 
Lira  .  . 

sterling  
na 

sterling^:  — 

Italy  

Gold.... 
Gold  

Gold  
Silver.... 

Japan  

Liberia  
Mexico    .  . 

Yen.... 

Dollar 
Dollar 



VALUES   OF    FOREIGN   COINS    IN    UNITED   STATES    MONEY       351 


VALUES  OF  FOREIGN  COINS  IN  U.  S.  MONEY— Continued 

(Proclaimed  by  the  Secretary  of  the  Treasury,  October  1,  1903) 


COUNTRY. 

Stand. 

Monetary  unit. 

f!t| 

"3  ~oc  o 

£V 

Coins. 

Netherlands... 
Newfoundland 
Norway 

Gold.... 
Gold  
Gold  

Florin  .. 

$0.402 
1.014 
.2f8 
.075 

.487 

1.080 
.515 

.193 
.268 
.193 

.044 
1.034 
.193 

Gold:  10  florins.    Silver:  ^,1   and  2}* 
Gold:  2  dollars  ($2.027).                [florins. 
Gold:  10  and  20  crowns. 
Gold:     X,    1   and  2   tomans    ($3.409). 
Silver:  X,  %,  1,  2  and  5  krans. 
Gold:  libra  ($4.8665).  Silver:   sol  and 
divisions. 
Gold:  1,  2,  5  and  10  milreis. 
Gold:  imperial,  15  rubles  (17.718V  and 
X    imperial,     7J£  r  u  b  1  e  a     1*3.859). 
Silver:  fc,  y,  and  1  ruble. 
Gold:  25  pesetas.    Silver:  5  pesetas. 
Gold:  10  and  20  crowns. 
Gold:     5,    10,    20,    50    and    100   francs. 
Silver:  5  francs. 
Gold  :  25,  50,  100,  250  and  500  piasters. 
Gold:  peso.  Silver:  peso  and  divisions. 
Gold:   5,  10,  20,  50  and  100    bolivars. 
Silver:  5  bolivars. 

Dollar 

Crown  

Persia  

Silver.... 
Gold... 

Kran  

Sol.. 

Portugal  
Russia  

Spain  
Sweden  
Switzerland  — 

Turkey  
Uruguay 

Gold  
Gold  

Gold  
Gold  
Gold  

Gold  
Gold  
Gold  

Milreis.... 
Ruble  

Peseta 

Crown  

Franc.  
Piaster  

Peso 

Venezuela  

Bolivar  

*The  coins  of  silver-standard  countries  are  valued  by  their  pure  silver  contents,  at 
the  average  market  price  of  silver  for  the  three  months  preceding  the  date  of  this  circular. 

tThe  "British  dollar"  has  the  same  legal  value  as  the  Mexican  dollar  in  Hongkong1, 
the  Straits  Settlements,  and  Labuan. 

tThe  sovereign  is  the  standard  coin  of  India,  but  the  rupee  ($0.3244^)  ia  the  money  of 
account,  current  at  15  to  the  sovereign. 


352  NEW   BUSINESS   ARITHMETIC 

STATUTORY  WEIGHTS  OF  THE  BUSHEL. 


STATES  AND 
TERRITORIES. 

EC 

<U 
^ 

£ 

60 
60 

g 

(X 

56 
56 

4 

32 
32 

>, 

JO 

a 
M 

48 
47 

:  &  \  Buckwheat. 

£  £  I  Shelled  corn. 

1 

§ 
c 
o 

<J 

£ 

'I 

V. 

0 

1 

60 
60 

c 

0 

'£ 

0 

f. 
(j 

"5 

c 
t 

t 

c 

i^ 

H 

05 

1 

60 
60 

Apples. 

Flaxseed. 

Millet  seed. 

T 

>. 

,C 

I- 

1 

u 
> 

JO 

United  States.... 
Alabama  

70 

=55 

56 

Alaska 

60 

60 
60 

Arizona  

60 
60 
60 
60 
60 
60 

56 
56 
54 
56 
56 

32 
32 
32 
32 
32 

45 
48 
50 
48 
48 

52 

4( 

5_ 
48 

54 
56 
52 
S( 
56 
=56 

"70 

60 

57 

57 

60 
60 

"SO 

56 

"so 

60 

45 
45 

Arkansas  

Colorado  

70 

60 
60 

57 
52 

50 

60 
60 

"48 

55 

Connecticut  

Dist.  of  Columbia 
Florida  

60 

60 
60 
60 
60 
60 
60 

56 

56 
56 
56 
56 
56 
56 

32 

32 
32 
32 
36 
32 
32 

56 

60 

48 
47 
48 
48 
48 
48 

52 

56 
56 

Sfi 

70 
70 

60 
60 

56 

57 

54 
55 

c60 
60 

48 

56 

50 

45 

60 

Georgia  

Idaho          .     ..   . 

42 

52 
50 

56 
56 
56 

"70 
d68, 

60 
60 
60 

57 
48 

55 

55 

"60 
60 

45 

56 
56 

"so 

45 
45 

60 
60 
60 

Indiana  

Indian  Territory. 
Iowa  

60 

60 
60 
60 
60 

56 

56 
56 
f32 

32 

32 
32 
32 
30 

?fi 

48 
4* 

1 

52 

50 
56 

56 

56 
56 
S6 

70 

70 
*70 

60 

60 
60 

57 

57 
57 

55 
60 

60 

60 
60 

48 
48 

56 

56 
56 

SO 

50 
50 

45 

45 
45 

60 

60 
60 

Kansas 

Kentucky  

Louisiana 

Maine  
Maryland..!  

48 

56 

60 
56 

52 

50 

60 

44 

.. 

.... 

45 

Massachusetts  .. 
Michigan  

60 
60 
60 
60 

60 
60 
60 

56 
56 
56 
56 

56 
56 
56 

52 
32 
32 
32 

32 
32 
32 

48 
48 
48 
48 

48 
48 
48 

48 

48 
50 
48 

52 

52 
52 

56 
56 
56 
56 

56 
56 
56 

"70 
70 
72 

70 
70 
70 

60 
60 
60 
60 

60 
60 
60 

52 
54 

57 

57 
57 
57 

48 

52 
55 

42 

55 

60 
60 
60 
60 

60 
60 
60 

48 
48 
50 

1-48 
MS 

55 
56 

56 

56 
56 
56 

*% 

48 
50 

50 

"so 

45 
45 
45 

45 

45 
45 
45 

60 
60 
60 
60 

60 
60 
60 

Minnesota  

Missouri.          .   . 

Montana  

Nebraska  

Nevada 

New  Hampshire. 
New  Jersey  
New  Mexico  

60 
60 

56 
56 

32 
30 

"48 

50 

56 
56 

.... 

60 
60 

57 

.. 

62 
60 

50 

55 

55 
55 
56 

56 
56 

64 

60 
60 
60 

60 
60 
60 
60 

"so 

50 

45 
42 

45 
42 

New  York..  .   . 

60 
60 
60 

60 
60 
60 
60 

56 
56 
56 

56 
56 
56 
56 

32 
32 
32 

32 
32 
32 
32 

48 
48 
48 

48 
48 
46 
47 

48 
50 
42 

50 
\2 
42 
48 

56 
56 
56 

56 
56 
56 
56 

"70 

68 
70 

60 
60 

60 
60 
60 
56 

57 
52 

55 
52 

50 

60 

60 
60 

60 
"60 

60 
60 

48 
50 

'4s 

North  Carolina.. 
North  Dakota.... 

Ohio  

Oklahoma  
Oregon 

Pennsylvania.  .  .  . 
Philippines  
Porto  Rico  

Rhode  Island  
Samoa  

60 

56 

32 

48 

48 

56 

70 

60 

50 

50 

60 

48 

56 

50 

45 

60 

South  Carolina.. 
South  Dakota.... 
Tennessee  

60 
60 

56 
56 

32 
32 

48 
48 

42 

50 

56 
56 

70 
70 

6052 

6056 

60 
50 

60 
60 

'so 

56 
56 

'so 

42 
45 

60 
60 

LEGISLATIVE 
ENACTMENTS. 


Act  July  18,  1866. 

Tariff  act,  1897. 

Act  Feb.  18,  1891. 

Comp.  Laws,  1864-71. 
Act  Mar.  30,  1887. 
Code  and  Stat.,  1886. 
Gen.  Stat.,  1891. 
Gen.  Stat.,  1902. 
Acts  1853,  1867,  1896. 
Webb's  Laws,  1868. 

U.  S.  Stat.,  1896. 
Stat.,  1901. 
Code,  1895. 
Penal  Laws,  1897. 
Laws,  1899-1903. 
Rev.  Stat.,  1899-1901. 
Rev.  Stat.,  1897. 

Rev.  Code,  1897,  and 

Laws,  1902. 
Gen.  Stat.,  1901. 
Gen.  Stat.,  1888. 
Rev.  Laws,  1884-1897. 
Rev.  Stat.,  1883,  Sup. 

1895,  Act,  1897. 
Code,  1888,  and  Sup. 

1890-1900. 
Rev.  Laws,  1902. 
Com.  Laws,  1897. 
Rev.  Stat.  1897. 
Code,  1892,  and  Act 

Mar.  12,  1900. 
Rev.  Stat.  1899. 
Stat.  1888,  1901. 
Com.  Stat.,  1901-1903. 

Pub.  Stat:,  1901. 
Gen.  Stat.,  1895. 

Gen.  Laws,  1902. 
Act,  Jan.  31,  1885. 
Code,  1899,  and  Act, 

Mar.  1901. 
Rev.  Stat.,  1902. 
Rev.  Stat.,  1903. 
Code,  1902. 
Digest,  1700-1901. 
Metric  system. 

Do. 

Pub.  Laws,  1900. 
English  Weights  and 

Measures. 
Laws  of  1903. 
Stat.,  1901. 
Act,  1887. 


STATUTORY   WEIGHTS   OF   THE   BUSHEL  353 

STATUTORY  WEIGHTS  OF  THE  BUSHEL— Continued. 


d 

4 

STATES  AND 
TERRITORIES. 

1 

sd  corn. 

on  cob. 

.2 

U 

I—) 

1 

ri 

I 
s 

1 

1 

** 

-o 

JS 

1 

LEGISLATIVE 
ENACTMENTS. 

«i 

u 

2 

S 

^ 

s 

d 

en 

0 

s 

c 

a 

X 

0 

> 

* 

& 

0 

a 

3 

23 

J3 
V3 

3 

£ 

O 

* 

£ 

P. 

.^4 

U 

Texas..  . 

60 

S6 

V- 

48 

4? 

56 

70 

60 

57 

55 

60 

45 

56 

SO 

45 

60 

Act,  Apr.  18,  1901. 

Utah.        .   .. 

Vermont  

60 

56 

V, 

48 

48 

56 

60 

5? 

60 

6? 

46 

45 

60 

Stat.,  1894. 

Virginia  

60 

V) 

48 

5? 

56 

70 

56 

57 

55 

60 

45 

56 

50 

45 

60 

Code,  1887,  and  Act, 

Feb.  24,  1898. 

Washington  

60 

S6 

V 

48 

4? 

56 

60 

45 

56 

60 

Stat.,  1897. 

West  Virginia... 

60 

56 

32 

48 

52 

56 

60 

60 

56 

45 

60 

Code,  1899. 

60 

56 

"P 

48 

50 

56 

70 

60 

57 

-P 

60 

50 

56 

50 

45 

60 

Stat    1898  and  Act 

Mar.  30,  1901. 

Wyoming 

c  Velvet  beans  in  hull,  78. 
d  Before  Dec.  1,  70. 
€  May  1  to  Nov.  1,  68. 


f  So  in  statutes,  but  an  evident  error. 
e  Japanese  barnyard  millet. 


ANSWERS 

ADDITION 

Article  34. 

6.  13054. 

22.  $15667. 

38.  $22290. 

2.  889. 

7.  17059. 

23.  10060  Ibs. 

39.  695  head. 

3.  698. 

8.  3127. 

24.  $15762. 

$5698. 

4.  967. 

P.  31945. 

25.  $641. 

40.  $5155. 

5.  898. 

10.  122223. 

26.  $9079. 

41.  $196910. 

6.  6546. 

11.  469294. 

27.  $5285. 

42.  40000. 

7.  786. 

12.  2601786. 

28.  4305  bu. 

43.  26520. 

8.  766. 

IS.  15448707. 

25.  4619. 

44-  23029. 

P.  9657. 

14.  2134. 

30.  4915. 

45.  176597. 

W.  $583. 

15.  11932. 

31.  4320. 

46.  1106771. 

Article  35. 

&  186. 

•16.  149271. 
17.  $3162. 
.15.  $21367. 

32.  4623. 
33.  3871. 
34.  39267. 

47.  1349248. 
48.  18366751. 
49.  15971078. 

3.  1492. 

19.  32515  ft. 

35.  $11024. 

50.  7556628. 

4.  2715. 

00.  77604. 

36.  $8304. 

51.  4187383. 

5.  9767. 

21.  504689. 

37.  $435. 

SUBTRACTION 

Article   41. 

12.  62114  bricks. 
13.  50435  yds. 

ilO.  21078. 
(  11.  142. 

22.  1902001. 
23.  $1482. 

2.  32. 
5.  72. 

Article  42. 

\12.  762301. 
13.  138. 

24.  $5457. 
25.  $4251. 

4.  55. 

2.  335. 

14.  4786. 

2ft  $4315. 

5.  542. 

5.  2561. 

15.  36824. 

27.  $9860. 

(5.  261. 

4.  561. 

1ft  22988. 

28.  $4644. 

7.  712. 

5.  3769. 

17.  89093. 

29.  $2948. 

5.  $232. 

ft  269. 

18.  296853. 

30.  $1288. 

5.  $235. 

7.  4509. 

19.  15744. 

31.  1250. 

0.  $2855. 

5.  1288. 

20.  4373. 

32.  $1316. 

/.  2307  bu. 

9.  30616. 

21.  988606. 

33.  $683.65. 

34.  $498.30. 

35.  $23107.02. 

MULTIPLICATION 


Article  43. 

2.  3248. 

3.  7308. 

4.  7348. 

5.  16310. 

6.  50550. 

7.  20909. 


8.  25632. 

9.  41616. 

10.  13140. 

11.  27738. 

12.  42115. 

13.  44289. 
14-  25374. 


15.  131235. 
1ft  327872. 

17.  163215. 

18.  194076. 

19.  348096. 

20.  222848. 

21.  348921. 

354 


22.  10588  gal. 

23.  $13225. 

24.  $1911. 

25.  $2072. 
2ft  $32778. 

27.  768  mi. 

28.  $261051. 


ANSWERS 


355 


Article  49. 
t.  17155. 
3.  16668. 
4.  13936. 
5.  54128. 
6.  113542. 
7.  1067616. 
8.  15824. 
ft  1007616. 

10.  407000. 
77.  5460200. 
72.  5031110. 
13.  5254000. 
14.  10800000. 
75.  17313936. 
16.  $171784. 
77.  $208656. 

18.  $51121. 
70.  792000. 
20.  8820000. 
21.  $34692. 
00.  $153832. 
23.  152000  Ibs. 
04.  53640  Ibs. 
25.  $16560. 

00.  205821  gal. 
27.  545622  cu.  in. 
28.  52752  Ibs. 
05.  208250  cents. 
30.  7878000  steps. 
31.  770400  words. 
32.  846720  Ibs. 
33.  2016000  cents. 

Addition,  Subtraction  and  Multiplication 

Article  50.  ±  $102.  8.  $27.  70.  $7700. 

38400  cents.  5.  $2865.  9.  $261.  13.  $11960. 

$595.  6.  B,  $600.  70.  1296  miles.  74.  $310. 

$344.  7.  $171.  77.  $200  gain.  75.  $5025. 

DIVISION 


Article  56. 

19. 

1162. 

10. 

212,  Rem.  92. 

07. 

$176. 

0 

3. 

432. 
312. 

20. 
21. 

1324. 
1214. 

11. 
12. 

958. 
7198. 

Article  58. 

'/. 

110. 

22. 

420. 

13. 

1489,  Rem.  33. 

0. 

6034,  Rem.  3d 

5. 

3124. 

23. 

2853. 

74. 

329916. 

3. 

25. 

6. 

3212. 

24. 

4754. 

75. 

14142. 

4. 

19,  Rem.  20. 

1. 

1221. 

25. 

16227. 

16. 

12152,  Rem.  9. 

5. 

15,  Rem.  65. 

8. 

9. 

4312. 
3102. 

Article  57. 

17. 
18. 

1444. 
8862. 

6. 

7. 

478. 
75,  Rem.  550. 

10. 

20120. 

2. 

213. 

19. 

463**. 

8. 

469, 

11. 

10203. 

3. 

34. 

20. 

329. 

Rem.  1470. 

12. 

10420. 

4. 

67. 

21. 

479AV- 

9. 

350. 

13. 

1011. 

5. 

247. 

22. 

535*}. 

10. 

1285, 

IS. 

430. 

6. 

314. 

23. 

128. 

Rem.  2080. 

16. 

735. 

7. 

48. 

24. 

$108. 

11. 

75. 

17. 

832. 

8. 

135. 

25. 

$96. 

12. 

$240. 

W. 

382. 

9. 

344. 

26. 

«HI 

Addition 

,  Subtraction, 

Multiplication  and 

Division 

Article  59. 

10. 

516. 

18. 

B,  $4200  ;  C, 

05. 

45  yards. 

1. 

$154. 

11. 

$18394. 

$15780;  all 

26. 

2474. 

£ 

$981. 

12. 

$2953. 

$20940.  ' 

27. 

$1490. 

.5. 

12. 

13. 

12. 

19. 

Gained  $13. 

28. 

$8269. 

* 

390. 

74. 

80. 

20. 

20  yrs. 

29. 

$10185. 

5. 

$712. 

75. 

$8. 

21. 

$9150. 

30. 

450  sheep. 

6. 

$336. 

16. 

$3468. 

22. 

$4. 

$5050. 

7. 

240. 

17. 

Daughter 

23. 

Grocer  owed 

.9. 

$120. 

$12923;  each 

farmer  12  cts. 

.9. 

$2904. 

son  $13763. 

24. 

15  cents. 

FACTORING 

Article  67. 

6. 

5,7. 

11. 

2,  2,  3,  3,  3. 

16. 

3,  7,  11. 

j 

3,  3. 

7. 

2,  3,  7. 

12. 

2,  2,  2,  3,  5. 

77. 

2,  2,  2,  2,  2, 

$'. 

2,  2,  3. 

8. 

2,  5,  5. 

13. 

2,  2,  31. 

3,3. 

4- 

3,  2,  3. 

9. 

3,  2,  11. 

14. 

2,  3,  31. 

18. 

2,  3,  7,  7. 

5. 

3,  3,  2,  2.           10. 

2,  2,  2,  2,  2,  3 

.    15. 

5,  5,  3,  3. 

19. 

3,  3,  3,  11. 

356 


NEW   BUSINESS   ARITHMETIC 


20.  2, 

2,  3,  5,  5.        25.  2,  2,  2, 

2,  41.       30.  2,  3,  3,  7,  23. 

34.  2,  2,  11,  79. 

21.  5, 

7,  11.              20.  2,  2,  3, 

3,  3,  7.    31.  2,  2,  29,  37. 

35.  2,  5,  17,  31. 

22.  3, 

5,  31.              27.  19,  67. 

32.  3,  2,  29,  53. 

30.  2,  2,  3,  19,  3,  13. 

23.  3, 

5,  5,  7.             2&  2,  2,  2, 

5,  73.      33.  3,  11,  13,  19. 

37.  11,  29,  43. 

24.  2,  2,  7,  23.          0P.  3,  449 

CANCELLATION 

Article  70.          5   54 

9.  49. 

12.  60. 

2.  11 

6.  21. 

10.  $76. 

13.  $2. 

3.  16 

7.  48. 

11.  24. 

14.  96. 

4.  24.                        3.  161. 

GREATEST   COMMON   DIVISOR 

Article  72.          4   14 

7.  6. 

10.  14. 

&  19.                        5.  19. 

8.  56. 

11.  60. 

3.  4. 

0.  13. 

9.  4. 

LEAST 

COMMON  MULTIPLE 

Article  76.          5   J260. 

8.  8400. 

11.  300. 

2.  2835.                    0.  288. 

S.  224. 

12.  90. 

3.  5040.                    7.  2520. 

10.  240. 

13.  378. 

4.  960. 

FRACTIONS 

Article  93.          5   21 

10.  -^w°  . 

5.  H,  I!,  iS,  H. 

2.  *, 

H,  H,  ft.        ft  22. 

1L  ?i' 

ft    284,   ft,  sV  A. 

3.  f, 

ft*>*    I  fit 

/<?     JLiyUL 

7.  5ft,  /A,  i¥«, 

1:1 

£  %" 

/  A     JL8  (LBJL 

T^0>    T20> 

8.  tH»,  tHt,  t!!8 

6.  ffV                       11.  411.                     Iff.  -V-. 

fill,  ttt«. 

7.  11                      10.  83?. 
Article  94.        18.  347J. 

17.  -¥-. 

1ft  H4- 

0     S-7.fi-      fiU.0       630 
**•     7"J(X>     720>     720' 

MB,  fltf,  ?S«- 

(2        6 

14.  72f. 

IP.  -•*/-. 

10.  ||,  f^,  -f^5-, 

f     Ij 

15.  188|. 

#0      5..JJ.6 

~44V~,    fl- 

t  if 

10.  37. 

f  1.  -3rV  . 

11.  ti,  -w-,  it 

5.  Xv                            Article  96.        ||  ~^ 

I!'  iv 

ft  if 

7;  i 

2.  -V-. 

g^.    -JLl^j6-8^. 

*  lie',  m!  ili- 

.  }' 

O       «l 

3.  *f°. 

J25.  -L7^-L-. 

13.  A,  T<&,  T¥ff, 

o.   g- 

p      61 

Fj-                    4.  -Bt4. 

^g    JL^lA.. 

T¥O. 

10!  j; 
j 

4                   5'  -W  • 

0     -^y*0 

irticle  95.          7]  i||o' 

Article  97. 
«.  ft,  H,  11- 

*'  iff,  fit',  III: 

<g   4 

8.  3M-°-. 

3.  i0,  it,  «• 

25   -JL   -W-,  i-J, 

3.'  8|.                        9.  m* 

4-  23|. 

4-  W,  H,  W,  It- 

j^,  tt,  it. 

Article  98. 
g.  2J. 

4^  1|J. 
5.  ft 
^.  3^4. 
7.  2ft. 


Article  99. 

g.  i 


tit 


7.  3ft 
•A  13H. 


Article  102. 

g.  2f 
3.  31 


5. 


7.  7$ . 

8.  If. 
P.  7. 

JO.  3f f. 

JJ.  5ft 

Jg.  $67f 

J4.  2840f. 

J5.  3853|. 

Jo.  11271. 

J7.  $7i 


19.  i 


?176i 
Article  103. 


g. 


Article  106. 

a 


5. 


ANSWERS 

Addition  of  Fractions 


357 


11. 


38|. 

32#. 

25AV 


J5.  27||. 

16.  69». 

J7.  $19A- 

J&  248f. 


J4.  478^r.  21.  5208A- 

Subtraction  of  Fractions 


JO.  3«. 
JJ.  10^. 
Jg.  1544 


17. 

18.  $3i 

19.  $4|. 
gO.  $4^. 
gJ.  $46A- 
22.  $40|. 


Multiplication  of  Fractions 

7.  647f|. 
A  193ft 


12. 
36. 
86|. 
85. 

& 

455. 


12.  3570. 


14. 


17. 


12. 


14. 


I  1077A 

[.  i  6 

?'.  1792! 
108. 

567.  18.  ^fW- 

$1545|.  19.  i. 

$1388f  gO.  A- 

$51|.  gJ.  i 

gg  128 

Article  104.        &  72  " 

I  24.  H' 

A.  g5.  108. 

3f.  27.  267A 

51f. 

Division  of  Fractions 
2^.  Article  109. 

$A.  g.  H. 


ta 

?:!!: 


gg.  $248ft 
24.  128645463Ty. 


?.  1856  A  bu. 

$776f. 
g7  1794 
28.  996^ 


$ 


g7. 


cts. 
cts. 


?.  ill- 


g&  166rV 

£9.  24ft 
on  $37^4-1 


28.  Ill 

29.  233^. 

30.  5AV 

33!  253||. 

34.  834^. 

35.  $1105|f 
3^.  $10i|- 

37.  54^V. 

38.  703B 

39.  7533$ 

40.  $104||. 
4J.  1097H- 
4g.  $1080. 

43.  74214  cts. 

44.  $12ft 

45.  308|  cts. 

46.  502f  cts. 

47.  1728||  cts. 

48.  $H- 

49.  21HH  gain. 


JO.  5&. 
JJ.  74|. 
Jg.  5&. 
J3.  2f 
J4.  ||. 
J5.  5j|. 
16.  f|. 


358 


NEW   BUSINESS    ARITHMETIC 


77.  iVs. 

2.  if- 

23.  If  yds. 

45.  Cost  $683L 

18.  fr. 

$    g»j» 

24-  f 

sold  $802/4\, 

20.  I*. 

4i  83A.  ' 

25.  2f. 

gain.$11945g. 

27.  Hf. 

5.  17/!),  T¥O»  T¥O, 

2ft  $87i 

4ft  4  days. 

0®        45 
<**•    704« 

T¥O. 

P7     <tRl 

#  1  .     *pO~<j' 

47.  $4577  SV 

23.  fa. 

ft  5H. 

28.  300. 

48.  36  ft. 

24.  1A- 

7.  55HJ. 

2P.  $646. 

49.  A  360,  B  320. 

30.  180. 

50.  $5800,  $1305. 

2ft  TiV 

27.  21. 

70i  422fS. 

37.  9. 
32.  192. 

57.  85V 
52.  12  da. 

28.  If 

W.  2H. 

33.  $5090H- 

53.  A  $2310,  B 

25.  Ito- 

72.  14if 

34.  $13f. 

$2800,  C  $1050. 

30.  $4^. 

73.  27iVj. 

35.  $i 

54.  $150,  $90. 

37.  10. 

74   $46^4 

3ft  334. 

55.  Lost  $2. 

32.  6. 

75.  Sotlf. 

37.  $3^. 

5ft  Buggy  $80, 

33.  9. 

7ft  10. 

38.  A  168,  B  112. 

horse  $100. 

34.  $8. 

77.  $70. 

39.  $7f. 

57.  A's  $96,  B's      • 

3ft  $30. 

18.  24. 

40.  $3. 

$120,  C's  $144, 

37.  $40. 

79.  47riftfr- 

41.  $472^0. 

D's  $90. 

Article  110. 

20.  $2i 
27.  $32. 

42.  40. 
43.  A  $208,  B  $156. 

58.  91 
59.  A  440,  B  352. 

7.  f 

22.  $136i 

44-  2|.     - 

60.  $21114^1 

Decimal 

Fractions 

Article  117. 

Article  118. 

7ft  5fa. 

70.  1291.5154. 

2.  .6. 

2.  i 

77.  107*. 

77.  7590.153. 

3.  .625. 

3.  A. 

72.  5038.4514. 

4.  .875. 

4.  i- 

19    16^o 

73.  37.047. 

5.  .9375. 

5.  f  k 

20.  143HS- 

14.  197.79985. 

ft  .208J. 
7.  .325: 

Article  119. 

75.  87.0885. 
7ft  $25.059. 

8.  ,053f 

^      8 

2.  1.4697. 

77.  $1541.86. 

P.  .107*. 

0;  It. 

3.  1.527. 

18.  93.6375. 

70.  .072|. 

4.  12.4203. 

19.  921.3087. 

77.  .008. 
72.  .00375. 

72!  136^0- 

5.  45.5345. 
ft  $23.86. 

20.  22.5625  yds. 
$13.8625. 

73.  12.375. 

73.  f 

7.  448.335. 

27.  5407.06444. 

14.  42.1875. 

74.  f 

8.  1465.856. 

22.  10756.78876. 

75.  200.015. 

75.  TV. 

9.  9468.5566. 

Subtraction 

of  Decimals 

Article  120. 

7/128.615. 

72.  $27.33. 

77.  824.175. 

2.  .2551. 

5.  194.567. 

73.  $1717.916. 

18.  11.0408. 

3.  .3844. 

9.  8093.9282. 

74.  16.0838. 

19.  106.18125. 

4.  10.1586. 

70.  77.779. 

75.  8.9991. 

20.  28.375875. 

5.  7.6719. 

77.  114.144. 

7ft  43.1875. 

27.  75.825753. 

ft  $13.075. 

Multiplication  of  Decimals 

Article  121. 

5.  312.1065. 

9.  3787.8025. 

73.  1. 

2.  19.27206. 

ft  4.687225. 

70.  .049. 

14.  $111.24375. 

3.  .2674968. 

7.  20.788302. 

77.  21.025. 

75.  1.63215. 

4.  92.752. 

8.  1031.921605. 

72.  .0001495. 

16.  $52.46875. 

ANSWERS 


359 


Division  of  Decimals 


Article  122. 

2.  4.5. 
3.  $4.6. 

4.  7.8  feet. 
5.  23.5. 

0.  .084.                    77.  425. 
7.  .215.                    12.  2.7. 
5.  8300.                   13.  21500. 
P.  480.                     74.  15.278+. 
70.  18600.                 75.  .02. 

70.  1450  bushels. 
77.  32  machines. 
18.  6350. 
19.  172300. 
00.  3020. 

Review  Problems 

Article   123. 

7.  122.099645. 
2.  6188.311478. 
3.  573  acres. 
4.  $1680. 
5.  $524.04. 

0.  124.9875.             77.  .00034375. 
7.  999999.999999.    12.  1. 
8.  .09775.                 13.  341.45. 
9.  720.352035.          14.  107  barrels. 
70.  $137.32005.         75.  {.  . 

70.  146  1  V 
77.  .012. 
18.  .65013054+. 
19.  $203.29|i 
20.  3.461+  or  &? 

UNITED   STATES   MONEY 

Addition 

Article  133. 

2.  $940.785. 
3.  $134.93. 
4.  $523.03. 

5.  $31.135.                 8.  $442.35. 
0.  $2835.185.             9.  $8426.48. 
7.  $4182.52.             70.  $11. 

11.  $282.75. 
12.  $207.675. 
13.  $100.65. 

Subtraction 

Article  134. 

£  $111.88. 
3.  $83.749. 

4.  $999.989.               7.  $2951.06. 
5.  $168.087.               8.  $50.90. 
0.  $576.56.                9.  $764. 

70.  $672.65  loss. 
77.  $2.42. 

Multiplication 

Article  135. 
2.  $182.25. 

3.  $582.25.                5.  $14.87. 
|.  $7240.                   0.  $444.70. 

7.  $1891.774. 
8.  $64.375  gain. 

Division 

Article   136. 
£  $.56. 
3.  $45. 
4.  $3.874. 

5.  $.32.                      9.  $.13. 
0.  475  barrels.        70.  124rV  bushels. 
7.  $72.                     77.  $.872}|. 
8.  $66.374. 

12.  $.27. 
13.  $.75. 
14*  $.224. 

SHORT  METHODS 

Article  138. 
2.  $109. 
3.  $156. 
4.  $156.25. 
5.  $94. 
6.  $2236.66|. 
7.  $  152.18f. 
5.  $97.20. 
9.  $10.724. 
70.  $4413.33£. 

Article  139.         3.  $226.151. 
2.  53  Ibs.                 4.  $101.36|. 
3.  192.9  doz.            5.  $48.692. 
4.  50f  bushels.        &  $41-782. 
5.  210  Ibs.                7.  $56.874- 
0.  72.5  acres.            #•  $44.16. 
7.  309|  acres.  -      &  $61.50J. 
5.  1495  Ibs.             JO-  $24.22405. 
Article  140.       11-  $47.8486. 
2.  $75.67. 

Article   141. 
2.  $58.6635. 
3.  $5.264. 
i  $2.738125. 
5.  $10.2648. 
0.  $1048.58325. 
7.  $377.806. 
&  5141611. 
S.  $99.36. 
70.  $52.93J. 

360 


NEW   BUSINESS   ARITHMETIC 

BILLS 


Article  145. 

1.  $438.14. 
2.  $16.73. 
3.  $53.81. 
4.  $59.06. 

5.  $906.81.                5.  $18.01  J  amt. 
6.  $65.02.                70.  $89.20  amt. 
7.  $123.28.               77.  $186.7985  amt. 
8.  $7.04J  amt.         70.  $40.71  amt. 

13.  $226.09. 
74.  $258.57^. 
75.  $195.49. 
16.  $177.28. 

Review  Problems 

Article  146. 

1.  $623.37*. 
0.  $406. 
3.  $45.25. 
4.  $841.48. 
5.  $2679.60. 
6.  $220.20. 
7.  $.33J. 
&  $10.33J. 
P.  $12.  gain. 
10.  $10.17. 
77.  $127.80. 

12.  $358.40.              24.  $292.  16|. 
13.  $39.12f              25.  $3.24  loss. 
14.  $330.75.               26.  $69.9H. 
75.  $3066.82.            £7.  $20.  12J, 
16.  $806.25.              28.  .5. 
17.  $1701.                 00.  $29.5974. 
18.  $.55.                    50.  45  minutes. 
19.  $26.75.                57.  iV 
00.  187  head.           32.  $81.872. 
07.  $1.                      33.  $4.94J. 
00.  $53331.                54.  1.464375. 
05.  $73.45. 

55.  $62.83i  gain. 
36.  174.8952  gal. 
57.  $42880. 
,-$49560.     sales 
of  matting. 
$214760.  sales 
$8   J  of  carpeting. 
'  1  $161070.    cost 
of  carpeting. 
$25167.18| 
^expenses. 

REDUCTION   OF   DENOMINATE   NUMBERS 

Article  155. 
8.  22547  far. 
4.  £32  15s.  8d. 

5.  10058  far.             7.  £18  lls.  lid. 
6.  253  far.                &  79971  far. 

9.  £6  15s.  4d. 
70.  342720d. 

Avoirdupois  Weight 

Article  160. 

1.  302  Ibs. 
2.  4500  Ibs. 
3.  8253  oz. 
4.  54787  dr. 
5.  1719998  dr. 

6.  43  cwt.  7  Ibs.     70.  1  T.  1  cwt.  26 
7.  6  T.  6  cwt.                Ibs.  1  QZ. 
8.  4  T.                    77.  $1061.04. 
9.  2  cwt.  52  Ibs.     70.  $94.01. 
2  oz.  2  dr.          13.  $9.55f. 
74.  $15. 

75.  24  T.  10  cwt 
16.  $2.55. 
77.  $39.09f. 
18.  $49.21  J. 
19.  $297.45. 
00.  $166.91*. 

Troy  Weight 

Article  161. 
1.  23040  gr. 
2.  835  pwt. 
5.  79606  gr. 

4.  6  pwt.  2  gr.          0.  $54.20. 
5.  5  Ib,  7  oz.  19      7.  $2549.40. 
pwt.  9gr.             5.  $62.50. 

9.  14  oz. 
70.  $14iV 

Apothecaries*   Weight 

Article  162. 

1.  gr.  28800. 
2.  33171. 
5.  gr.  12642. 

4.  41b.                     7.  471. 
5.  §8  91  gr.  4.         8.  10  Ib.  §1    35 
6.  41b.  §6  91               31. 
gr.  1. 

9.  $68.40. 
70.  $218. 
77.  $4212. 

ANSWERS 


361 


Comparison  of  Weights 


Article  164. 

4.  78  Ib.  11  oz.  18    7.  $92. 

11.  12  Ib.  lOrfos  oz. 

1.  21^  Ibs. 

pwt  8  gr.             8.  82|  oz. 

12.  26  Ib.  4^  oz. 

2.  $1667.50. 

5.  $12.                       9.  43|  Ib. 

75.  Yes.     1240 

5.  92  Ibs.  4  oz.  6 

<?.  266H*  oz.          70.  $22f 

Troy  grains. 

pwt.  16  gr. 

Long  Measure 

Article  168. 

5.  5145  rds.              8.  14  mi.  7  fur.  26 

12.  $23.80. 

/.  103  in. 

2.  260  in. 

tf.  3657  in.                     rds.  3  yds.  2  ft 
7.  1  fur.  24  rds.  2    5.  $500.90|. 

75.  $369.90. 
14.  65  in. 

3.  1600  rds. 

yds.  1  ft  4  in.  10.  2230  in. 

75.  2213.12  mi. 

4.  2785  rdsr 

77.  240  leagues. 

16.  8700. 

Surveyors'  Long  Measure 

Article  169. 

3.  6600  ft.                 5.  2  mi.  3  ch.  3 

0.  10208.88  ft. 

L  17772.48  in. 

4.  7832  yds.                   rd.  9  1. 

2.  182239.2  in. 

Square  Measure 

Article  172. 

8.  1  sq.  yd.  8  sq.    15.  $6.21. 

25.  $151.80. 

1.  7776  sq.  in. 

ft  19  sq.  in.       16.  $234.60. 

26.  $96.07. 

2.  1600  sq.  rd. 

9.  3  sq.  yd.  2  sq.    17.  $27.12. 

27.  $252. 

3.  102400  sq.  rd. 

ft  2  sq.  in.         18.  1004  sq.  ft. 

£5.  $63.22. 

4.  3312  sq.  in. 

10.  12  sq.  yd.  5  sq.  19.  $186.14. 

20.  $13.44. 

5.  241128*  sq.  ft. 

ft  56  sq.  in.       20.  $100.67. 

30.  $49.18. 

6.  412247748  sq. 

71  49  sq.  ft.             £7.  $163f 

57.  426  ft. 

in. 

12.  75  A.                   0&  $602.25. 

32.  27  ft. 

7.  6  A. 

13.  600  sq.  yd.         £3.  51}  yd. 

55.  5964|  sq.  fL 

14-  54  sq.  yd.           #.  $56. 

5^.  6400  sq.  ft 

I 

Board  Measure 

Article  175. 

4.  250  ft                  8.  1620  ft. 

77.  $12.83. 

7.  16  ft. 

5.  72  ft                     9.  378  ft. 

12.  $25.03. 

2.  18  ft 

6.  138|  ft                70.  $11.52. 

75.  184.96. 

3.  42  ft. 

7.  1306|  ft 

Surveyors'  Square  Measure 

Article  181. 

3.  65  A.  2  sq.  ch.     7.  $332. 

70.  360  A. 

1.  23040  A. 

5000  sq.  1.             8.  $11180. 

11.  9ii 

2.  3880240  sq.  1. 

4.  $5579.76.                   $1128.60. 

$621.18. 

5.  $3500.                   P.  400  A. 

Cubic  Measure 

Article  184. 

5.  128  cu.  yd.         10.  $41.07. 

14.  $25.60. 

1.  147  cu.  ft 

0.  5C.  32  cu.  ft.      77.  128  ft 

15.  1520  cu.  ft, 

2.  30C.  24  cu.  ft. 

7.  $11.14.                 12.  1  hr.  48  min. 

33440  brick, 

3.  78  cu.  ft. 

8.  15C.                    13.  $50.91. 

$284.24. 

4.  466|  cu.  yd. 

P.  125  cu.  ft 

362 


NEW   BUSINESS   ARITHMETIC 


Article  187. 
7.  104  pt. 
0.  69  pt. 

3.  10080  gi. 

4.  191  gi. 

5.  633  pt. 


1. 


Article  188. 

l  48. 


Liquid  Measure 


6.  158  gal.  3  qt. 

7.  54  bbl.  14  gal. 
2  qt.  1  pt. 

8.  317  bbl.  14  gal. 
2  qt. 


9.  $362.88. 

10.  $14.49. 

11.  44. 

12.  14553  cu.  in. 
'3.  20YV  gal. 


Apothecaries'  Fluid  Measure 


2.  f  3  736. 

3.  £3  1997. 


14.  1436f?  gat. 
75.  935rB7  gal. 
16.  718H  gal. 
77.  329}  gal. 


i  M  223182. 

5.  f    2  f 3  6  M  28. 


Cong. 

9  f  3  5. 


2  O2  £? 


Article  189. 
7.  128  pt. 
0.  368  pt. 
#.  164  pt. 

4.  511  pt. 

5.  6bu. 


Dry  Measure 

6.  2  pk.  7  qt.  1  pt.  70.  $1.56. 


7.  44  bu.   3  pk.  1 
pt. 

8.  767  pt. 

9.  $3.20. 
70.  $9.12. 
71  $1.90. 


$2.16. 
14.  $2.05,  6  cts. 
75.  36557.14  cu. 

in. 
16.  7ibu. 


77.  2256f  bu. 
nearly. 

18.  $137.85. 

19.  $108. 

20.  19ft.  5.3  +  in. 

21.  $34.65. 

00.  9  ft  11.46+  in. 


Comparison  of  Dry  and  Liquid  Measure 


Article  191. 
7.  27  gal.  1  qt.  + 
2.  5  bu.    2  pk.  1 

qt.  2  pt.  - 


Article  194. 

7.  7200  sec. 
0.  7680  min. 
3.  200732  sec. 


3.  Paid 
$2.92,  gain 
$.90. 

4.  $1.63. 


5.  The  latter, 
$.61. 

6.  302.4  cu.  in 


Time  Measure 

5.  98845  min.  9.  1  mo.  1  da.  1  77.  105. 

6.  164392938  sec.  min.        12.  88. 

7.  4  hr.  3  min.  70.  5  mo.  6  da.  19  13.  198. 
20  sec.  hr.  28  min.  20  14.  91. 


4.  12547638  sec.   8.  2  wk.  4  da.  7  hr.  5  min.   sec. 


Article  196. 

7.  15336". 
&  136132". 


Circular  Measure 


3.  3°  25'  46". 

4.  120°. 

5.  95°. 


6.  10800'. 

7.  12448*  stat 
mi. 


8.  315T75  geog. 
mi. 


Article  197. 

7.  $1728. 

0.  $.36. 

&  $17.75. 

4.  $4. 

5.  $9.52. 
&  $259.20. 


7.  65  yr. 


Miscellaneous 


66ft. 


70.  12}$  lb. 
77.  30ft  lb. 
12.  22§f  lb. 
/&  30jW  lb. 
7^.  1.96  lb. 
15.  1.28  lb. 

;<?     (  28  X  42. 

,.     (  32  X  44. 
11  '    J64. 
18.  9  and  10. 
No  diff. 

ANSWERS 


363 


Review 


Article  198, 

$7.68. 

$7.60. 

33. 

16. 

$122.40. 

$53.37?. 

17. 

$331   i)l  KJ 


77.  $1.44.  22.  37  hhd. 

12.  5^c.  gal. 

13.  85*  bu.  nearly.  23.  1204  sq.  ft. 
7i  9  ft.+. 

15.  34  wk. 

16.  $120.96. 
77.  100800. 
75.  $13.78. 

16.75.  $8.68U. 
20.  $34.02. 


21.  $135. 


2*.  42. 

25.  24. 

26.  $7.92. 

27.  1  yr.  10  mo. 
19  da.  9  hr. 

28.  29|  cu.  ft.,  608  36.  $90.68f. 

sq.  ft.  37.  Gain  $39.86. 

38.  4»VA  lb. 


DEDUCTION  OF  DENOMINATE    FRACTIONS 


Article  200. 
2.  1  ft.  n  in. 
&  1  wk.  5  da.  10    75.  6  gal.  2  qts. 

hr.  40  in  in. 
^.  5  cwt.  30  11). 

12  oz.  12^  dr. 
€.  8  cwt.  57  lb.  2 

oz.  44  dr. 

7.   11  A.  96  sq.  rd.  4.  2ri*o- 
A'.  3  A.  77  sq.  rd.     5. 
9.  7  bu.  tf.  a1*- 

70.  9'  54".  7.  &. 

11.  ?10  31  gr.  15.84.  5.  **, 

12.  2   fur.  6  rd.  1     9. 
vd  2  ft  9J  in.     70. 


13.  2  oz. 

74.  1  lb.  4  oz. 


3.68  gi. 
Article  201. 
»}* 

5  (*'  0  0  • 


Article  202. 


9. 


Article  203. 
2.  .7322+. 
5.  .0502+. 

4.  .0034+. 
5  .9375. 
0.  .609375. 
7.  .6041+. 

5.  .000056+ 
P.  .0931+. 

10.  .0012. 
//.  5.38+. 


Review   Problems 


Article  204. 
1.  $34.98. 
£  $8.51. 
5.  $20594.80. 
4-  »\\. 
5.  $2.05. 
<?.  21  A.  Ill  sq: 

rd.3sq.yd.  6sq. 

ft.  45-%  sq.  in. 


7.  $9314.80. 

8.  .2844+. 

0.  600  sq.  rd. 
70.  258.44. 
77.  .0021175. 

12.  $9782. 

13.  .00084+. 


14-  3600. 
15.  15  da. 
7tf.  86400. 
77.  $163821. 

18.  $225.30. 

19.  $858.08. 


20.  £5516s4(4&?8i)d. 

21.  $2310.58. 

22.  $1554.63. 

23.  Liverpool 
$1671.84. 

24.  $3723.73. 


ADDITION   OF   COMPOUND  NUMBERS 


Article  205. 

2.  £40  4s.  9d.  1 
far. 

3.  14  T.  3  cwt.  24 
lt>.  12  oz.  3  dr. 


4-  177  bu.  1  pk.  7  qt.    in. 


5.  26  mi.  244  rd. 

5  yd.  4  in. 

6.  280  A.  142  sq. 
rd.  12  sq.  yd. 

6  sq.  ft.  29  sq. 


7.  17°  16'  37".         70.  7  fur.  18  rd   15 

8.  $116.83.  ft.  6f  in. 

9.  53  hhd.  40  gal.  77.  6A.  113  sq.   rd 
1  qt.  1  pt.  21  sq.  yd.  5  sq. 

ft.  66i  sq.  in. 


364 


NEW    BUSINESS    ARITHMETIC 


SUBTRACTION  OF  COMPOUND  NUMBERS 


Article  206. 

2.  11  Ib.  11  oz.  3 
pwt.  15  gr. 

3.  32  yr.  273  da. 
10  hr.  46  min. 
19  sec. 

4.  57  bu.  2  qt.  1  pt. 

5.  55  gal.  1  gi. 


6.  2  T.  15  cwt.  94  10.  2  yr.  6  mo.  21 
Ib.  6  oz.  da. 

7.  £363  4s.  lid.   11.  1  mo.  18  da. 

1  far.        12.  1  rm.  16  qr.  8 

8.  197  A.  129  sq.  sh. 

rd.  22  sq.  yd.  7  18.  47°  17'  22". 
sq.  ft.  72  sq.  in. 


14.  1  yr.  7  mo.  16 
*  da.  5  hr. 

15.  9  cwt.  10  Ib. 

16.  8  wk.  15  hr.  12- 
min. 

17.  26  gal.  1  qt. 


MULTIPLICATION  OF   COMPOUND  NUMBERS 


Article  207. 

4.  342  A.  114  sq. 

5.  94  gal.  3  qt.  3      7.  99  T.  6  cwt.  94 

t  41  bu.  1  pk.  6 

rd.  3  sq.  yd.  1 

gi- 

Ib.  2  oz. 

qt.  1  pt. 

sq.  ft.  37  sq.  in. 

6.  37  cu.  yd.  8  cu. 

3.  33  Ib.  7  oz.  11 

ft.  160  cu.  in. 

pwt.  12  gr. 

DIVISION 
Article  208. 

2.  3  bu.  2  pk.  6 
qt.  1  pt. 

3.  Ib.  1  §10  36 
gr.  19f 


OF   COMPOUND  NUMBERS 


4.  38  mi.  147  rd. 
3  yd.  2  ft.  5iV 
in. 

5.  2  cwt.  72  Ibs. 


6.  106  A.  106  sq. 
rd.  20  sq.  yd.  1 

sq.  ft.  72  sq.  in. 

7.  5  oz.  8  pwt.  8 


8.  52  bu.  3  pk.  5 
qt  If  pt 

9.  5  Ib.  5  oz. 
dr. 

10.  10. 


LONGITUDE   AND  TIME 


Article  210. 
2.  2  hr. 
3.  1  hr.  6  min.  16 

11.  2  hr.  8  min.        19. 
15fc  sec. 
12.  4  hr.  5  min. 

49  min.  33f 
sec.  past  7  p. 
m. 

Article  211. 
1.  8  min.  past  4 
a.  m.  Wednes- 

sec. 

17i  sec.              20. 

13  min.  17{f 

day. 

4.  52  min.  44  sec. 

13.  7  hr.  38  min. 

sec.  past  10  p. 

2.  52  min.  past 

5.  37°  30'. 

8  sec. 

m. 

noon  next  day. 

6.  5  hr.  8  min.  1 

14.  5  hr.  34  min.      21. 

10  min.  19  sec. 

3.  32  min.  19& 

sec. 
7.  1  hr.  19  min. 

6f  sec. 
15.  35  min.  18|  sec.  22. 

past  11  a.  m. 
58  min.  7^ 

sec.  past  11  p. 
m.  Monday. 

12|  sec. 

past  11  a.  m. 

sec.  past  4  p. 

4.  14  min.  56{| 

8.  1  hr.  4  min. 

16.  12H  sec.  past 

m. 

sec.  past  8  a. 

44f  sec. 

3  p.  m.               23. 

59  min.  13  sec. 

m.  next  day. 

9.  2  hr.  37  min. 

17.  40  min.  12  sec. 

past  10  a.  m. 

5.  3  p.  m.  Satur- 

39T\ sec. 

past  6  p.  m. 

10  min.  47  sec. 

day. 

10.  36  min.  28H 

18.  33  min.  4j£ 

past  4  p.  m. 

sec. 

sec.  past  7  p.  m. 

Saturday. 

REVIEW   PROBLEMS 


Article  212. 

1.  12540. 

2.  553357. 

3.  30. 

4.  $1.52. 

5.  $1.60. 

6.  6  bu.  2  pk.  2 
qt. 


7.  49m*. 

8.  $96055.31-1 . 

9.  $373J. 

10.  168. 

11.  49. 

12.  4  hr.  26  min. 
24  sec. 

13.  2  rd. 


16.  502  gal.  1  qt. 
3gi. 

17.  $2.58. 

18.  .2278-K 

19.  2  Ib.  7  oz.  19 
pwt.  9  gr. 


20.  .3918+ . 

21.  45  rd.  3  yd. 
2  ft.  9f  in. 

22.  I  cwt.  45  Ib. 

23.  225  A.  127  sq. 
rd.  27|  sq.  yd. 

24.  203  rd.  3  yd. 
1ft.  15,1  in. 


ANSWERS 


365 


25. 

6|  in. 

30.  44  yr.  4  mo. 

on  the  pre- 

36. 

1418.9+bu. 

26. 

.04093. 

12  da. 

vious  day. 

37. 

9+bu. 

27. 
28. 

$17.75+. 
$37.27+. 

31.  1  hr.  39  min. 
30T45  sec. 

33. 

34. 

July  29,  1895. 
20  A.  37A  sq. 

38. 
39. 

1536.01+. 
29  Ibs  2  oz. 

29. 

$10164. 

32.  9  min.  36  sec. 

rd. 

40. 

$50.97. 

past  6  p.  m. 

35. 

3284f$. 

Article  218. 

2.  4. 


RATIO 


9.  12. 
70.  17. 
77.  31.32. 


12.  A- 

.  2. 


73. 


3f. 


Article  226. 

&  114U. 
3.  $400. 


5.  $131*. 


SIMPLE  PROPORTION 

6.  $58.80.       77.  $25.30.  16.  16|  da. 

7.  34.         12.  5  mo.  13  da.  77.  $17.50. 

8.  19  hr.       13.  $2.09i  18.  $2.10. 

9.  600  bu.      14.  249f  ft.  19.  8|  Ibs. 
70.  5096.        75.  90  men.  20.  15. 


COMPOUND  PROPORTION 


Article  228. 

2.  8rV 
5.  30. 
4.  $18J. 
5.  $9804.26. 
6.  $396. 

7.  8  ft. 
8.  $1600. 
0.  $118|. 
70.  $512.58. 
77.  5^  hrs. 

12.  $731.25. 
13.  $35.64. 
7i  $128. 
15.  4f  f. 
70.  7*V  da. 

. 
18. 


$51.08. 
65*f 
5^V  ft. 
258. 
36ff  da. 


MEASUREMENTS  USED   IN   BUSINESS 


1. 
2. 
3. 
4. 
5. 
6. 

Article  240. 

$270.56. 
$31.66. 
1800. 
68H  bd.  ft 
$233.73. 
$760.32. 

7. 
8. 
9. 
10. 
11. 
12. 
13. 

$1447.04. 
$6566.40. 
67  iVg  perch. 
$27.30. 
$30.47. 
133}  ft,  $2.87. 
$10.60 

14. 
15. 
16. 
17. 

18. 

164340. 
$1314.72. 
3'  U". 
15  sq.  ft.  128 
sq.  in. 
127440  bricks. 

19. 

20. 
21. 
22. 
S3. 

24. 

e 

< 
< 
( 
< 

\ 
] 

>4.5818+  perch 
5314.84. 
5365.63. 
5823.20. 
5227.50. 
$114.98. 
L8300. 

366 


NEW   BUSINESS   ARITHMETIC 


PERCENTAGE 


Article  251. 

2.  $24. 

3.  $114. 

4.  $259.20. 

5.  $518.40. 

6.  $612.50. 

7.  810  bu. 

8.  10660  men. 

9.  3981.3  ft. 
10.  4042.5  Ib. 
77.  $41.28. 

12.  1674.75  bu. 
IS.  M. 
14.  .19|. 


9. 
10. 
11. 

12. 

2. 
3. 

5. 
6. 
7. 
8. 
9. 


16.  $.1881. 

17.  $3.36.  10. 

5688.80.  11. 

1410,  $4230.     72. 

#16.  13. 

21.  $10.60. 
20.  25*,  $1125. 
23.  Jones  $841.50.   14. 

Brown  $486.88. 15. 
24*  I,  i.  #. 

25.  $5.30.  77. 

2ff.  $5.40.  I& 

27.  45*. 

28.  3085f  bu. 

29.  3152. 
50.  $666f. 

Article  252.       19. 

1.  $112.  20. 

2.  320  bu. 

3.  1215  yd.  2. 
I.  238  Ib.                 3. 

5.  $178|.  4. 

6.  226|  yd.  5. 


28|  doz. 
$179. 
$90. 
1218. 
14  bbl. 
$368. 

Article  253. 
$324. 
$5.76. 
182  gal. 
150  ft. 
2812$  yd. 
$360.."' 
$5917 
$168.74. 
$105.82. 
767.25  bu. 
198  sheep. 
$6.25. 

$427.30  lost. 
$3845.70  re- 
mained. 
$4749.50. 
548. 
$18290. 
$3637J. 
Wife    $13500, 


6.  $2100.  13. 

7.  $1800. 

8-  $900.  14. 
9.  400  sheep,  310 

sheep  left.  15. 

10.  600  yds.  16. 

11.  $3600,  $3888.  17. 

12.  Smith  $800,  18. 
Brown  $3000. 

13.  $140.40.  19. 

14.  $1190. 

15.  Claim  $3900,  2. 
com.  $93.60.  3. 

16.  $20000.  4. 

17.  $1193.75.  5. 
1$.  Bought  160,  6. 

had  460.  7. 

19.  $10,  $4.50.  8. 

20.  Had  $2000,  9. 
gave  wife  $150,  10. 
gave  daughter  11. 


1st  year  $600, 

2d  year  $500. 

First  cost 

$1000. 

Lost  $18.331. 

$53331. 

1600. 

Men  54,  women 

24,  children  9. 

$7800. 

Article  256. 

5*. 

12*. 

7*. 

25*. 

40*. 

33J*. 


$62.50. 
Article  255. 

2.  $500. 

3.  $300. 

4.  $200. 

5.  $500. 


elder  son  $6300,  6.  3400ft. 
younger  son       7.  3000  bu. 
$6300,  daugh- 
ter $18900. 
$31229.41. 
$301.50. 
Article  254. 
5250. 
1400. 
2250. 


Article  257. 

1.  66  horses. 

2.  $254.76. 

3.  $1.47r- 

4.  $134.90. 

5.  $24.67. 
0.  $1062. 

7.  1053  bu. 

8.  $5525.52. 

9.  $2.12. 
10.  $14.81. 
71  $53.01. 
12.  $5504. 


15. 
16. 
17. 
18. 

19. 


21. 

22. 

23. 
24. 
25. 


REVIEW 

$85.50,  $71.25. 

$448,10*. 

$500. 

$9300, 

93  shares, 

35  *  paid  out, 


8.  $1600. 

9.  1191  Ib. 

10.  Cost  $225, 
selling  price 
$267.  21. 

11.  Principal  $700,  22. 
Interest  $56.      23. 

12.  200  sheep,  10    24. 
A,  9  B,  6  C. 

PROBLEMS 
27.  $6300. 


8J*. 

25*. 

30*. 

22*  *. 

20*. 

5*. 

16*. 

6i*. 

60  *,  $516. 

12*,  15*. 

40*,  3.5*,   25*. 

West  28*, 

Packard  26  *, 

Young  24  *, 

Retained  22  *. 


28.  8J*. 

29.  $2681.87. 

30.  $1600.80. 

31.  $4269.67. 

32.  15*. 


65  %  remained.  33.  1062£  bu. 


38. 
39. 
40. 
41. 
42. 
43. 


$197.20. 


15  & 
$20  loss. 
3900  bu.  B, 
2958H  bu.  C. 
$180,  15*. 
$5260.39. 
$300. 
$89.60. 


84.  25*. 

35.  45  *  currency,  44. 
35  %  gold, 

20*  silver. 

36.  $2496.  45. 

37.  Horse  $156.52,  46. 
wagon  $250.44. 
reaper  $313.04. 


75*. 
10*. 


$16000. 
$100. 

$2000,  $3000. 
$155357*. 
$1920,  $2880. 
A>  $691.20, 
B's  $576, 
Cs  $720. 
Oysters  $92, 
fisli  $41.40, 
clams  $33.35. 
$36824. 
15*. 


ANSWERS 


367 


PROFIT   AND  LOSS 


Article  264. 

18.  $1080.08.             32.  25*. 

48.  38f  *. 

0.  $22.20. 

19.  $280.                   33.  8*. 

49.  $72. 

3.  $25.20. 

00.  $440.                   34.  16|*. 

50.  $2019.40. 

4.  $47.60. 

07.  $310.63.               35.  16*. 

57.  $9,  $6.60. 

5.  $42.53. 

00.  $106.                   30.  16*. 

50.  A  $163.04. 

0.  $530. 

03.  $3250  Hall.        37.  $10. 

53.  $279.06. 

7.  $417. 

$3900  Miller.     38.  $11250. 

54.  '$76.50. 

8.  $30. 

$4524  Davis.      39.  $42.04. 

55.  $864. 

9.  $59.65. 

04.  7500  bu.              40.  $1499.88. 

50.  44*. 

JO.  $6.40. 

05.  $24.                    41-  27i*. 

57.  19^r*. 

77.  $460. 

00.  $65.                    40.  10*. 

58.  $112.50. 

70.  $300. 

07.  $1.19.                  43.  70|*. 

59.  10*. 

13.  $180. 

28.  $810.                  44-  $35.70.  . 

00.  $6675. 

74.  $120. 

29.  $27,  $9.              45.  $537.60. 

07.  $3525.72. 

75.  $11750. 

30.  $203.28.               40.  $1.50  gain. 

$3966.43. 

70.  $1600. 

37.  $502.91.              47.  $6.75,6*. 

00.  6*. 

77.  $1380. 

03.  9&*. 

MARKING   GOODS 

Article  267. 

n        \  8                             jj    m.   et 

1*    m.  oe 

7.  $5.76  w.  t.  i. 

'   yus.  as                               '   a.  tag 

1  '•    p.  ex 

7     *•  as                             70      CR 

1K      $M 

2   "*  bp 

>*•  °8                            id          i_ 

°'    $17.50 

n.  ao 

8  yu-  as                  **'  e-    e 

19.  o.  li 

3.  — 

•    os    ao                           ji     t5-75 

00.  b.  ex 

*£3 

/\     .at                                            $8.05 

*  5T                       75.  40*. 

07.  $1.043  c.  thi 
00.  g.  oe 

c     o.  rs 

70.  o.  pn                   JQ    $3.80 

03.  r.  gnf. 

. 

TRADE  DISCOUNT 

Article  275. 

7.  $5.60.                   70.  $164.15. 

18.  $48. 

0.  $507. 

8.  $2.54.                   73.  $252.67. 

19.  $25. 

3.  $15.75. 

9.  $259.20.               74.  $373.93. 

00.  $12. 

4-  $27.30. 

70.  35|*.                  75.  $42.34. 

07.  $8. 

5.  $156.05. 

77.  $384.75.               70.  $454.48. 

00.  h.  n  r. 

0.  $15.84. 

BILLS 

Article  280. 

4.  $410.96,                 7.  $36725.52, 

70.  $1839.63, 

7.  $40.75. 

$398.63,                     $34889.24. 

$1614.28. 

Article  281. 

S388.66.                8.  $1599.30, 

77.  $264.04. 

0.  $149.98, 

5.  $847.40,                     $1535.33, 

$258.76, 

$144.04. 

55805.03,  $797.23.       $1489.27. 

12.  $212.54. 

3.  $1935.03. 

0.  $873.17,                9.  $160.52, 

13.  $37.86. 

$1783.32. 

$804.63.                     $154.17. 

$37.10. 

COMMISSION 

Article  295. 

0.  $2.66.                   70.  $1756.30. 

18.  $1216. 

0.  $18.50. 

7.  $100.99.               73.  $495.85. 

19.  $1100. 

3.  $30.40. 

8.  $43.29.                74.  $138.46. 

00.  870  bu. 

4.  $2.57. 

9.  $37.15.                 75.  $175.68. 

07.  $960. 

5.  $5.75. 

70.  $37.13.                 16.  $820.52. 

00.  $817.26. 

368 


NEW   BUSINESS   ARITHMETIC 


.25.  $656. 

51 

£2.                       55.  4*                      45.  $390. 

.24.  250.                     52.  ! 

5641.48.              40.  6  JT.                      46.  i 

51897.27. 

25.  $1055.15.             55.  5 

51.20.                  41  $743.                   47.  5 

51033.69. 

27.  $400. 

54.  : 

5520.                   42.  5 

5790.91,               48.  i 

5319.35. 

28.  $650. 

55.  5 

5960.                         i 

5869.41.               49.  i 

5144.64. 

29.  100. 

50.  1500  bu.             45.  5 

510661.                50.  5 

52301. 

30.  600  bu. 

55.  3*.                    44.  5 

5280.                   51.  $564.73. 

45694-  lb. 

FIRE  INSURANCE 

Article  311. 

11.  J 

£3428.57*.           15.  Mutual  $621,         United  States 

2.  $160. 

54571.42f               Springfield  $828.     $10050,  Lancas- 

5.  $24. 

.72.  i 

52743.13.                 Local  $920,              ter  $16750, 

4.  $75. 

.75.  5 

5903.16.                  Commercial            Orleans  $6030. 

5.  $639. 

.74-  ^tna  $700,            $1242.                    17.  $7200,  $4698. 

6.  $21. 

Home  $980,       16.  Metropolitan    18.  \\%. 

7.  $93.65. 

Essex  $1225,         $12060,  Great       19.  } 

i* 

8.  $3160.80. 

Phoenix  $1470.      Western  $14740,  20.  3|  %. 

10.  $9200. 

American  $8710, 

MARINE   INSURANCE 

Article  315. 

4.  5 

53037.50.               8.  Paoli  $1659.38,      $1235.31, 

1.  $1912.60. 

5.  < 

562.18.                     Leipsic  $2655,          Litchfield 

2.  $1900. 

6.  5 

51028.13.                West  Baden            $2489.06. 

5.  $89.25. 

7.  5 

J90.49.                    $3171.25,  Custer 

LIFE   INSURANCE 

Article  325. 

4.  $60.90.                  7.  $150.30.              10.  $983.50. 

1.  $161. 

5.  $2036.70.               8.  $960.25.               11.  $6320. 

2.  $166.18. 

0.  $96.                       9.  $432.50.               72.  $65. 

5.  $168.75. 

REVIEW  PROBLEMS  IN  PERCENTAGE 

Article  326. 

10.  $457.14.               19.  $9500.                 25.  400  bu. 

1.  1U&                  11.  $2800.                 20.  $10.40.                29.  $167.75, 

2.  \ 

5149J.                  .72.  $2.00  A.  WX.      21.  19  #.                          18f  1  1 

5   ( 

54i- 

13.  8*.                     22.  ^ 

526.                     30.  $.80. 

4.  S 

53520. 

14-  $2.80.                  25.  $3640,  $3328.      31.  $64.29  gain. 

5.  5 

4801 

.75.  42*0.                  24.  $109.20  1'wise.  52.  56J  #. 

$   ! 

.70.  31B*. 

108.00  c'wise.  55.  2 

7iVff  $• 

7]  < 

52.80. 

17.  First  $1260,       2J.  $320.                  54.  $3500. 

&  33J  &                         Second  $1449.   #0.  $200.                  55.  $4900,  $5100. 

9.  $20. 

18.  $3021.74.            27.  $2575.                50.  $57. 

INTEREST 

Article  339. 

P.  $40.                     70.  $ 

,515.36.               25.  J 

2004.17. 

&  $21.20. 

10.  \ 

516.80.                 17.  $ 

5311.67.              24.  i 

5663. 

5.  $21.27. 

11.  ( 

574.60.            -    18.  5 

5379.32.               25.  5 

54980. 

4.  $43.20. 

12.  i 

520.48.                19.  i 

J517.50.               20.  5 

5360. 

5.  $19.20. 

13.  i 

718.75.               20.  5 

51496.24.                   Article  340. 

6.  $15.96. 

J<y-.     » 

1409.60.               21.  \ 

5554.70.                 2.  5 

11.06. 

7.  $86. 

15.  i 

5247.25.               22.  5 

5703.73.                5.  i 

51.29. 

8.  $21.60. 

ANSWERS 


369 


4.  $4.50. 

15. 

$8.42. 

25.  i 

£38.85. 

35.  $412.50. 

5.  $11.20. 

16.  $9.27. 

26.  ! 

548.83. 

35.  ; 

547.25. 

6.  $12.39. 

17. 

536.16. 

07.  5 

5481.25. 

37.  5 

519.84. 

7.  $.57. 

18. 

532,25. 

po     < 

52.88. 

33.  i 

533.25. 

3.  $1.23. 

19. 

523.52. 

0s.  i 

51.44. 

39.  < 

543.21. 

Q    ' 

51.33. 

20. 

594.03. 

30.  ; 

56. 

40.  < 

547. 

to.  I 

51  92 

21. 

536.49. 

31.  5 

51.80. 

11  i 

1147.68. 

n.  s 

5U2.'                  00.  $417.69. 

30.  < 

581.10. 

40!  i 

53.60. 

(0.  5 

531.20. 

23.  $107.80. 

33   S 

573.78. 

43.  < 

530.40. 

f3.  $3.76. 

04.  $43.20. 

34.  5 

51.79. 

44.  5 

513.34. 

(4.  $11.02. 

Sixty  Days  Method 

Article  341. 

6.  ! 

$2.67. 

11.  $11.67. 

15  i 

508 

0.  $2.80. 

7.  ! 

511.18. 

12.  $5.20. 

17!  i 

L32! 

3.  $2.65. 

8.  ! 

17.08. 

13.  $1.73., 

13.  ^ 

53.72. 

4.  $7.20.                   9. 

57. 

14.  $2.08. 

19.  5 

5.92. 

5.  $8.19. 

10.  $19.58. 

15.  $2.43. 

00.  j 

52.79. 

Six  Per 

Cent  Method 

Article  342. 

7.  $369.98. 

13.  S 

51297.66. 

13.  5 

£758.89. 

0.  $37.08. 

3.  $46.61. 

14.  5 

5865.56. 

19   ! 

51640.99, 

3.  $116.25. 

9.  $20.46. 

15.  5 

5128.23. 

00'.  5 

5346.16. 

4.  $379.44. 

10.  $9.08. 

15.  5 

5220.97. 

01.  S 

5207.18. 

5.  $550.67. 

11.  $620.64. 

17.  5 

51763.72. 

00.  S 

5819.58. 

6.  $88.05. 

10.  $2412. 

Cancellation  Method 

Article  343. 

5.  $17.28. 

S.  ^ 

557.67. 

13.  $1608.89. 

0.  $19.20. 

6.  $38.22. 

10.  J 

58.85. 

14.  $1095.75. 

3.  $ 

28.                       7.  $96.25. 

11.  S 

54.73. 

15.  $2609.86. 

4.  $188.75. 

3.  $44.80. 

10.  i 

577.58. 

•  x 

Common,  Bankers  and 

Exact  Interest 

Compared 

Article  344. 

7.  i 

19.68.      13.  \ 

51.46.                     19. 

£18  8s.  Id.  3  +  far. 

0.  $28.56. 

2.99.        14.  i 

55.10.                     20. 

£32  4s.- 

3.  5 

5.70. 

34.46.      15.  5 

54.33.                     01. 

£7  lls.  6d.  2  -far. 

4  5 

>.04. 

10!  i 

1.87.        15.  < 

5122.55.                 00. 

£2  17s.  lid.  2  +  far. 

5i  i 

5.07. 

11.  i 

.25.          17.  5 

57.09.                     23. 

£459  lid.  3  -far. 

6.  i 

.10. 

10.  5 

.02.          13.  £4  14s.  10d.2-far. 

Problems  in  Interest 

Article  345. 

7.  2  yr.  2  mo.  12          Article  346. 

9   8  So 

0.  2  yr.  6  mo. 

da. 

2.  8*. 

m  6*! 

3.  1 

yr.  2  mo.  12 

8.  March  19, 

3.  1%. 

11.  10*. 

da. 

1907. 

4.  4*. 

10.  8*. 

4.  3  yr.  7  mo.  6 

9.  Sept.  28,  1904.    5.  10  *. 

Article  347. 

da. 

10.  Nov.  30,  1902.     6.  \\%. 

0.  $500. 

5.  8  mo.  4  da. 

11.  June  28,  1909.     7.  9*. 

3.  $319.52. 

6.  27  da. 

10.  May  31,  1906.     3.  8*. 

4.  $218. 

24 

% 

370 


NEW   BUSINESS   ARITHMETIC 


5.  $136. 
6.  $433.61. 
7.  $760. 
8.  $103.33. 
9.  $799.32. 

70.  131 
77.  500  bu. 

Article  348. 

£  $240. 

3.  $370. 

4.  $1170. 
5.  $180. 
(5.  $650. 

7.  $550. 

8.  $2175. 
P.  $95. 
70.  $286. 
77.  $728. 

Annual  Interest 

Article  350. 

2.  $915.14. 
3.  $428.65. 

4.  $1284.24. 
5.  $507.73. 
0.  $687.42. 

7.  $1342.37. 
8.  $214.92. 
9.  $174.88. 

70.  $3709.99. 
77.  $1395.85. 

Compound  Interest 

Article  352. 
0.  $129.30. 
5.  $212.42. 
4.  $1019.86. 
5.  $146.08. 
6.  $399.65. 
7.  $1239.08. 

8.  $9.17. 
P.  $35.15. 
70.  $128.50. 
77.  $398.03. 
70.  $1091.75. 
13.  $10690.54. 
74.  $2805.86. 

75.  $500. 
16.  $5340. 
77.  $1000. 
18.  $680. 
75.  $460. 
00.  $850. 
• 

21.  $1250. 
00.  $18.22. 
23.  $.44. 
24.  $.13. 
25.  $1.58. 
0tf.  $762.20. 

Commercial  Paper 

Article  367. 
1.  $715.85. 

£  Aug.  19,  1905 

$875.48. 

.     3.  Feb.  28,  1906, 
$1279.25. 

4.  $883.07. 
0.  June  15,  1905, 

Partial 

Payments 

Article  369. 

£  $262.88. 
&  $728.16. 
4.  $719.33. 
5.  $393.75. 
6.  $212.17. 

7.  $2904.54. 
8.  $923.04. 
9.  $995.35. 
10.  $11777. 
Article  370. 
1.  $425.50. 

£  $265.44. 
3.  $938.42. 
4.  $81.60. 
5.  $401.47. 
tf.  $1353.87. 
7.  $979.78. 

8.  $413.01. 
9.  U.  S.  Rule, 
$.21. 
70.  U.  S.  Rule, 
$1.09. 
77.  $559.69. 

Article  371. 
7.  $6625.38. 


Annual  Interest  with  Partial  Payments 

0.  $790.00. 


TRUE   DISCOUNT 


Article  375. 

0.  $170. 
3.  $940. 
1.  $810. 

5.  $1339.94. 
6.  400  bu. 

7.  $480. 
8.  $150.78. 

9.  $5.                       13.  $700. 
70.  $4.95.                  14.  $103.63. 
77.  Gain  $6.73.        75.  900  bu. 
12.  $107.52. 

BANK  DISCOUNT 

Article  379. 

5.  I 

517.39. 

9.  $2692.83. 

1905,  53  da  vs. 

0.  $3.30. 

6.  i 

562.63. 

70.  $193.34. 

$2.89,  $277."!  1 

5.  $3.70. 

7.  < 

5912.33. 

11.  July  12, 

Proceeds. 

4.  $2.80. 

8.  ! 

5459.30. 

ANSWERS 


371 


72.  Feb.  25,  1906, 

74.  June  5,  1906,      10.  $275.16  Pro- 

23.  $1200. 

111  days, 

65  dars,                     ceeds. 

24.  $1500  Face, 

$21.46  bank  dis 

.,      $38.03  bank  dis.77.  $1814.94. 

$1487.50  Pro- 

$972.79 Pro- 

$2068.16 Pro-    18.  $1006.82. 

ceeds. 

ceeds. 

ceeds.                 19.  $943.55 

25.  $360. 

73.  Oct.  1,  1905, 

75.  Apr.  26,  1906,   20. 

$608.11. 

20.  $593.42. 

r 

r8  days, 

115  days,           21.   $720. 

27.  $1196.64. 

$17.64  bank  dis 

i 

P8  bank  dis.,     22.  $552.92. 

$1339.16  Pro- 

$305.12 Pro- 

ceeds. 

ceeds. 

STOCKS  AND 

BONDS 

Article  403. 

77.  $409.50.               35.  112f. 

• 

L  for  1  A, 

7.  < 

^378. 

18.  $252,  $3348.        30.  8*. 

I  for  2  B. 

2.  5 

5304. 

19.  $20846.87.           37.  60. 

2  for  5  C 

3.  5 

5270. 

20.  < 

5408.50.               33.  $19000. 

50.  $27270. 

4.  J 

5247.50. 

27.  < 

5513.50.               39.  60. 

57.  $300. 

5.  < 

1182.25. 

22.  < 

51457.                 40.  52. 

52.  Latter  $85.50 

0.  ! 

5247. 

23.  5 

520830.                41.  40. 

53.  3 

5883.41. 

7.  $207. 

24.  i 

5840,  284  £.         42.  5 

54.  5 

5158.27. 

3.  $2288. 

26.  27  snares.           43.  5jV  %. 

55.  ! 

5187.50. 

9.  $3741.10. 

27.  $3300.                 44.  4$£. 

50.  5 

51056.25. 

70.  $6855. 

23.  41  shares.           45.  $262.50,  12A  %. 

57.  < 

5629.67. 

77.  $1642.20.             29.  $ 

51400.                 40.  < 

53.  5 

5128.50. 

12.  $7546. 

30.  $ 

59150.                 47.  $528,  5&V  %. 

5P.  $35827.50. 

73.  $4089. 

31.  < 

54315.31.             43.  Latter  &%. 

00.  $1059.54  Loss. 

74-  $1226.25.             32.  I 

500,  $18650.        4P.  $1000000  A, 

07.  $80, 

15.  $330. 

33.  300.                           $750000  B, 

02.  i 

^lilf^j  4r4a#. 

70.  $150. 

34.  * 

!6f  .                            $250000  C, 

$12445. 

DOMESTIC  EXCHANGE 

Article  410. 

9.  $223.50.              18.  $370. 

27.  $1229.52, 

7. 

5560.70. 

70.  $1875.50.             19.  i 

5465. 

23.  1500  bu. 

2.  ; 

5728.63. 

11.  $930.09.              20.  < 

51178. 

29.  i 

^510.64. 

3.  * 

51307.78. 

72.  $589.21.               27.  ! 

51849.15. 

30.  < 

J599.69. 

4   « 

51839.49. 

73.  $864.20.              22.  i 

5272.11. 

37.  i 

5947.91. 

5!  $627.75. 

14.  $326.42.              23.  1 

55772. 

32.  < 

5433.22. 

0.  $2817.10. 

75.  $1256.75.             24-  5 

56748.42. 

33.  $109.23. 

7.  $287.68. 

70.  $322.59.               25.  $333.91. 

34.  $1801.80. 

3.  $482.40. 

77.  $925.                   20.  $133.84. 

35.  20  shares. 

FOREIGN  EXCHANGE 

Article  415. 

0.  $492.83.              77.  $840.32. 

70.  £710. 

7.  $4332.08. 

7.  $5918.86.             72.  $80. 

77.  8000  marks. 

2.  $780. 

8.  $782.78.               73.  £583  12s.  6d. 

73.  £526  4s.  2d. 

3.  $660.34. 

9.  2200  bu.              74.  4193.98  fr. 

19.  $32,  1905.32  fr. 

4.  $1546.05. 

70.  $1320.                  75.  660  marks. 

20.  1021.27+  yd. 

5.  $375. 

NATIONAL  BANKS 

Article  422. 

$50000,  $12500    5.  $212565. 
to  $50000             0.  $2235,  $2115. 

8.  $643.25. 
9.  $3265,  $11885. 

7.  $62500, 

3.  3 

5480000,                7.  $21250, 

70.  $51400, 

$62500.                      3 

524000.                     $425000. 

$55897.50. 

2.  5  persons, 

4.  c 

Hi*,  $156.25. 

372 


NEW   BUSINESS   ARITHMETIC 


SAVINGS  BANKS 


Article  425. 

4. 

$1003.27. 

8. 

$1973.90. 

11. 

$243.90. 

1. 

$2.35. 

6. 

$352.92. 

9. 

$755.15. 

12. 

$493.69. 

2. 

$30.02. 

7. 

$787.64. 

10. 

$1910.63. 

13. 

$135.17. 

8. 

$992.94. 

TAXES 

Article  432. 

3. 

$5836.50. 

6. 

$1972.92. 

9. 

$184.97. 

/. 

$421.70. 

4. 

$12164.04. 

7. 

$1466.85. 

10. 

$329.87. 

2. 

$81.08. 

5. 

$467.10. 

11. 

.018. 

.09. 

CUSTOMS 

OR 

DUTIES 

Article  448. 

4. 

$318.36. 

8. 

$488.87. 

11. 

$2770.86;. 

1. 

$255.60. 

5. 

2641.79. 

9. 

$3754.25. 

12. 

$2197.80. 

2. 

$590.27. 

6. 

$209.91. 

10. 

$1897.54. 

13. 

24782.66.. 

3. 

$877.80. 

7. 

$222.61. 

EQUATION 

OF 

ACCOUNTS 

Article  456. 

10. 

Oct.  6. 

Article  457. 

10. 

April  1,  1904U 

2. 

April  10,  1905. 

11. 

May  8,  1905. 

2. 

April  27,  1905. 

11. 

$808.96. 

3. 

5  mo.  21  da. 

12. 

Aug.  20,  1905. 

3. 

April  2,  1905. 

12. 

$595.48. 

4. 

9  mo.  12  da. 

13. 

June  14,  1905. 

4. 

May  28,  1905. 

Article  458. 

5. 

Oct.  16,  1903. 

14. 

March  14,  1906.  5. 

Jan.  28,  1906. 

1. 

Auer.  21.  1905-.. 

6. 

Aug.  9,    1905. 

15. 

June  29,  1905. 

6. 

Jan.  2,  1905. 

2.  Tune  19  '.  1905. 

7. 

Oct.  15,  1905. 

16. 

May  13,  1905. 

7. 

Oct.  21,  1905. 

3. 

June  17,  1906 

8. 

Oct.  2,  1905. 

17. 

Oct.  28,  1905. 

8. 

July  30,  1905. 

$19.83. 

* 

9. 

June  23,  1905. 

18. 

July  1,  1905. 

9. 

Oct.  16,  1905. 

4. 

April  19,  1905* 

$499.69. 

CASH 

BALANCE 

Article  459. 

3. 

$1311.41. 

&.. 

$1188.63. 

4. 

$724.03. 

PARTNERSHIP 

Article  472. 

3. 

Jones 

Hammond 

C  $2935.88;. 

1. 

2001. 

$4552.40, 

$3844.65, 

D  $3114.44,. 

2. 

$1042.50. 

Brown  $3602.40, 

Siders 

Firm 

3. 

Smith  $3096.20. 

$3593.75, 

$11688.27. 

4. 

.28. 

4. 

F  $6308.08, 

Firm 

5. 

$2552.33 

G  $7067.07, 

$11544.05. 

Article  475. 

A  $1160.15, 

H  $6838.77, 

3. 

Stewart 

2. 

Gain  $920.35, 

B  $928.12, 

I  $6184.38. 

$4593.16, 

A  $406.22, 

C  $464.06. 

5. 

O  $4325, 

Nevins 

B  $514.13. 

6. 

Gain  $4835.36, 

P  $4342, 

$4543.66, 

3. 

Gain  $825, 

share  of  each 

Q  $4505, 

Barnard 

Fuller  $225, 

$1208.84. 

R  $4371. 

$3193.43, 

Irwin  $330, 

Article  473. 

Firm 

Diers  $270. 

2. 

C  $19099.60, 

Article  474. 

$12330.25. 

4- 

A  $792, 

D  $18849.60, 

2. 

Parker 

4. 

A  $2398.58, 

B  $561, 

E  $18699.60. 

$4105.65, 

B  $3239.37, 

C  $957. 

ANSWERS 


373 


5.  Jennings 

Collins                     $320, 

$3277.89, 

$1200, 

$1626.49.                   B's  cr.  int. 

Wilson 

Fuller  $792, 

4.  Tyler  $310.40,          $501, 

$5394.93, 

Clark  $948. 

Brady  $422.96,         C's  cr.  int. 

Farrel 

6.  Gain  $1009.80, 

Hess  $511.64.'           $649, 

$5038.83. 

F  $299.20, 

5.  20.0568  %,                  D's  cr.  int. 

5.  A  $5668.58, 

G  $336.60, 

A  $932.64,                 $876.25, 

B  $6331.42. 

H$374. 

B  $656.86,                 A's  cap. 

6.  Loss  $975.10, 

Article  476. 

6.  A  $707.69,                $296.96, 

A  $4743.69, 

2.  Hammond 

B  $675.85,                 B's  cap. 

B  $4716.55, 

$1030, 

C  $556.46.                 $1066.44, 

C  $8284.66. 

Cowles  $960. 

Article  477.              C's  cap. 

7.  White 

3.  Manning 

2.  W  $9353.11,             $802.91, 

$1848.86, 

$1480.11, 

G  $10470.11,             D's  cap. 

Murray 

Miller 

S  $14142.78.              $5701.69. 

$2651.14. 

$2394.20, 

3.  A's  cr.  int.           4-  Harding 

INVOLUTION 

Article  482. 

8.  .027.                    16.  i 

23.  1.27628. 

1.  324. 

9.  f|i                    77.  11529. 

24,  .000000001. 

2.  157464. 

10.  1.21665+.           18.  3888. 

25.  .00001936. 

3.  19.0096. 

11.  1.340095+.         19.  47  14. 

26.  16  yd. 

4.  31640625. 

1%.  rfStk-               20.  113  A  145  sq. 

27.  421875  cu.  in. 

5.  1.97382+. 

IS.  23||.                         rd. 

28.  19.19140625. 

6.  23.6196. 

14.  7776.                  21.  .000000000001. 

an        633  44  3_ 
*•'•     ToffSTSS- 

7.  1024. 

15.  301                    22.  .00000081. 

SQUARE  ROOT 

Article  489. 

6.  667.                    11.  \l 

16.  4.168+. 

2.  32. 

7.  625.                     12.  16|. 

17.  .094. 

3.  43. 

8.  1296.                   13.  .866+. 

18.  .0081. 

4.  65. 

9.  ,V                      14.  1.732+. 

19.  1.732+. 

5.  248. 

10.  5J.                      15.  .8164+. 

20.  11.180. 

Applications  of  Square  Root 

• 

Article  496. 

4.  146.86  +  ft.           7.  Width  53.15+ 

9.  452.54+  rd. 

1.  50  ft. 

5.  21  ft.  11  in.               ft,  length 

10.  187.46+  rd. 

2.  12.64+  ft. 

6.  80  rod,                      106.30+  ft 

11.  40.85+  ft 

3.  51.26+  in. 

320  rod.                8.  49.92+  ft 

CUBE  ROOT 

Article  497. 

6.  216.                    11.  9.75. 

15.  1.44+. 

2.  36. 

7.  359.                     12.  3.54+. 

16.  2.08+. 

3.  63. 

5.  441.                     13.  1. 

77.  2.35+. 

4.  126. 

5.  536.                    14.  1.25+. 

75.  |. 

5.  177. 

70.  630. 

Applications  of  Cube  Root 

Article  497. 

4.  999  in.                 6.  12  ft  10.8+ 

9.  8  ft.  6+  in. 

1.  39  in. 

5.  Depth  55.6+            in. 

10.  lit.  6.9+  in. 

2.  14.32  ft. 

in.,  length            7.  3  ft  8+  in. 

77.  8  ft.  8+  in. 

3.  57  ft 

111.  2  +  in.            8.  12150  sq.  ft 

374 


NEW   BUSINESS   ARITHMETIC 


MENSURATION 


Article  511. 

3.  203.71+  rd.               Article  532. 

4.  1435456f*  cu. 

1.  $200. 

4.  235.62ft               1.  198  sq.ft. 

yds. 

2.  $6503.91. 

5.  3  ft.                       2.  373^  sq.  ft. 

Article  538. 

3.  576. 

Article  520.         3.  27.0963  sq.  ft. 

/.  3631.6896  sq.  ft 

4.  $32.36. 

1.  1017.87+  ft         4.  600  sq.  ft 

2.  $45.24. 

5.  39^  yd. 

2.  10.  456+  A.                Article  533. 

3.  196663355.7504 

Article  514. 

3.  1A  20+  sq.  rd.    1.  425  cu.  ft. 

sq.  mi. 

1.  486  sq.  yd. 

4.  1963i  sq.  yd.        2.  4230.144  gal. 

Article  539. 

2.  672f  sq.  ft. 

5.  441  7"|  sq.  ft.        3.  5026f?  gal. 

1.  1767.15  cu.  in. 

3.  800  sq.  ft. 

Article  531.              Article  534. 

2.  14137.20  cu.  ft 

4.  $54. 

1  6  sq.  ft  108         1.  1728  cu.  ft. 

3.  2982.0656+ 

Article  519. 

sq.  in.                   2.  32616  cu.  ft. 

cu.  ft. 

1.  9243.7  ft. 

2.  36  sq.  ft.               3.  6946||  cu.  ft 

4.  354.08+  hhd. 

2.  376.99+  rd. 

METRIC  SYSTEM 

Article  543. 

9.  6.35  m.               16.  100  ha. 

23.  3.645  1. 

1.  763.217  km. 

10.  197.63  dm.         11.  .015004008 

24.  1000  g. 

2.  318462m. 

1976.3  cm.                cu.  m. 

25.  907.2  kg. 

3.  39,516,000cm. 

11.  56.38  a.               18.  14018.0036 

26.  11.023  Ib. 

4.  516.26m. 

.5638  ha.                   cu.  dm. 

27.  2204.6  Ib. 

.51626  km. 

12.  2187500  sq.  m.   19.  10001. 

28.  91000. 

5.  106.  25427  miles 

2187500  ca.        20.  $.066. 

29.  2|  s. 

6.  $168.75. 

13.  286.176  ha.         21.  $18205.92. 

30.  3  cu.  m. 

7o  1577.114km. 

14.  $12.83.                22.  6703.125  Dl. 

31.  46.328  cu.  m. 

If  771.14  hm. 

15.  5.  106383  -km.        67.03125  cu.  m. 

32.  G840  sq.  m. 

8.  16.9164m. 

^^RA^^ 

ff          OFTHE*^ 

• 

UNIVERS/TY 

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